Ireland outscored their French hosts by three tries to two, with Jonathan Sexton (2) and Andrew Trimble both crossing the whitewash, as Joe Schmidt's men twice came from behind in a thrilling title decider in Paris.
They finished level on eight points with Triple Crown winners England, who had earlier beaten Italy 52-11 on an action-packed final day, but the men in green were crowned champions thanks to a +10 scoring difference (+83 compared to England's +73).
Returning scrum half Maxime Machenaud was prominent in a strong opening quarter from les Bleus. He slotted two early penalties to open up a 6-0 lead, with his first kick going over off the left hand post.
The strong-carrying Mathieu Bastareaud got France on the front foot, but Ireland showed their mettle and replied with a try after taking the hosts through 11 phases.
Sexton's classy 21st-minute score came off a flicked pass from Chris Henry, and he did well to slip past Bastareaud's attempted tackle and reach the line.
The Ireland out-half missed the kickable conversion but the visitors were celebrating their second try just five minutes later as direct running from Brian O'Driscoll and Conor Murray set up winger Trimble's third try of the tournament.
It was a tremendous team score as a thrusting run from O'Driscoll got Ireland over the gain-line, then Murray sniped into open territory off the back of a ruck and Trimble timed his support run to perfection to collect the final pass and run in beside the posts.
Sexton converted for a 12-6 scoreline, however France landed a considerable blow on the half hour mark when Yoann Huget deftly batted a cross-field kick back for Brice Dulin to dot down in the right corner.
Machenaud, Sexton's Racing Metro club-mate, landed a fine conversion from wide out which was the difference between the sides at the break (13-12) with Sexton missing an injury-time penalty.
The unconverted place-kicks and missed tackles, combined with some loose kicking out of hand, would have played on the minds of Sexton and his team-mates, but they steadied the ship at the interval and hit the ground running on the restart.
Ireland have made a habit, in recent weeks, of scoring tries early in the second half and they added another to the highlights reel at the Stade de France.
Trimble split the French defence with a powerful surge up the right wing. He almost put the retiring O'Driscoll through for a fairytale try, the French getting back to deny him before captain Paul O'Connell's follow-up at the ruck gleaned quick ball and Murray fed Sexton for his second try of the night.
The gap was widened to 22-13 after Sexton had converted and tagged on a penalty, and Ireland's confidence was visibly growing as they chased their first away triumph under Schmidt.
France turned to their forwards to get them back in touch, a furious spell of carrying close to the Irish line ending with hooker Dimitri Szarzewski touching the ball onto the right hand post for a converted try.
That left Ireland holding onto a two-point advantage with 17 minutes left on the clock. It was a crucial juncture in the high tempo fixture and the influence of experienced heads like the immense O'Connell, Rob Kearney, who had a fine game at full-back, O'Driscoll, Rory Best and Gordon D'Arcy was so important.
Roared on by the thousands of Irish fans in the crowd, Schmidt also put faith in his youthful bench with Iain Henderson, Martin Moore, Jack McGrath and Ian Madigan - all aged 24 and under - called on to help Ireland get over the finish line.
Madigan came on for a groggy Sexton, who was injured when tackling the onrushing Bastareaud, and acquitted himself very well with some good covering and clearance kicks.
The tireless Jamie Heaslip, Devin Toner, Cian Healy and Henry stood tall in the forward exchanges as they combined with the fresh legs to repel the French in a defiant defensive display. Henderson earned his corn with a blockbusting tackle on Jean-Marc Doussain.
However, in events that mirrored the 2009 Grand Slam match in Cardiff, Ireland had to ride their luck as they entered the closing stages with a narrow lead.
Replacement Doussain sent a 70th minute penalty wide - much to the dismay of the home supporters - and number 8 Damien Chouly had a try ruled out after a forward pass from French skipper Pascal Papé.
Les Bleus also turned the tables in a scrum battle that had been going Ireland's way for much of the encounter - Mike Ross' pressure on Thomas Domingo had led to him being replaced at half-time.
Tension gripped the stadium as the home side won a last-minute scrum against the head, but Ireland turned to a well-honed play - the choke tackle - with Toner, Henry and O'Connell combining to hold up the monstrous Sebastien Vahaamahina and win a final turnover.
Referee Steve Walsh's final whistle was greeted with jubilation by the Ireland players, management team and fans alike as they celebrated a second Six Nations crown in five years and the country's 12th Championship stretching back to the late 1800s.
It was such a fitting way for Brian O'Driscoll to bow out of international rugby, the evergreen centre picking up his second successive man-of-the-match award to boot.
There were emotional scenes afterwards as the 35-year-old reflected on his silverware-winning finish in the green jersey - 14 years on from playing a starring role in Ireland's last win in Paris.
Giving his reaction tonight, O'Driscoll said: "It was last-leg stuff and I know now why I'm packing it in because 80 minutes is a long bloody time at international level, particularly with guys like Mathieu Bastareaud running at you - it's no fun!
"But it's a magnificent feeling (to win the Championship again). When it properly sinks in tomorrow when we get home and I'm able to reflect upon it, I'm sure there will be a few tears.
"There were a few tears earlier on when Joe gave his team talk. It was quite emotional."