In addition, last year's graduates, David Heffernan and Daniel Qualter, have also signed a 12-month extension on their current deals with the senior squad.
The latest contracts make it 15 Connacht players who have committed their future to the province in recent months.
Commenting on the Academy graduates, the westerners' head coach Pat Lam said: "It's fantastic that we will have these local-born and Irish qualified young men fully integrated into the senior squad next season.
"Jack Carty was given the promotion earlier in the season and it's great to be able to bring Finlay, Darragh and Conor on board now.
"I've seen first-hand the work ethic and the commitment from these boys who are constantly striving to improve their game and themselves.
"We know that they are all capable of stepping up to the next level when needed. If they continue to work hard, I have no doubt that they will go from strength to strength in the coming months.
"Our Academy, under Nigel (Carolan), has proven to be very profitable in identifying and developing young talent for the good of the Connacht and Irish teams and the latest four graduates are testament to that.
"On Heffernan and Qualter, Lam added: "We have also offered contract extensions to both Dave and Danny who made the step up from the Academy last year.
"Dave has really impressed us this year especially with the speedy transition he went through to go from playing in the back row to hooker.
"He has shown us his commitment and drive to make the shift a success and we have seen his good work on the pitch in recent games.
"As a young lock, Danny possesses immense skill and talent and we believe that, with more time, he has the potential to compete with the experienced players around him."
Heffernan joined the Connacht Academy in 2011 and after two years, progressed to the senior set-up.
The Ballina native went to school in Blackrock College before playing with Connacht at Under-19 and Under-20 levels. He then went on to represent Ireland Under-20s, playing against France in the 2011 U-20 Six Nations.
While the 23-year-old started his rugby career as a back rower, last season he began the conversion to the hooker position where the coaches felt he showed a lot of potential.
Heffernan, who plays his club rugby with Buccaneers RFC, earned his first senior cap fo Connacht in March 2012 when, at age 21, he was named to start against the Scarlets at blindside flanker.
This season at hooker, he has made 10 appearances off the bench in the RaboDirect PRO12 and scored his first competitive try against Munster at Thomond Park last Christmas.
Qualter spent three years with the Connacht Academy before advancing to a senior contract with the province last year.
The Athlone-born lock, who plays with club side Buccaneers, has represented Ireland at Under-18, Youth Schools and Under-19 levels and played 15 times for the Ireland Under-20s.
Last season, the 22-year-old made his senior debut for Connacht, coming off the bench against Edinburgh at the Sportsground.
The performance of the 6ft 5in second row earned him a further two senior appearances in the Heineken Cup games, both home and away, against French side Biarritz Olympique.
This season, he was a regular starter with the Connacht Eagles in the British & Irish Cup and the interprovincial clashes.
Leader was recruited to the Academy under Carolan at the start of the 2012/13 season. That same week in October 2012, the 20-year-old Galway native was selected to line out at full-back in his first competitive game for the province against the Ospreys, the then league champions.
Playing his club rugby with Galwegians RFC, Leader went on to represent Ireland at Under-19 and U20 level.
Last summer, he was part of the Ireland Under-20 squad that went to the 2013 IRB Junior World Championship in France where he was named at full-back against eventual pool winners New Zealand.
This season, under Pat Lam, Leader, who can play full-back, wing or centre, has already earned ten caps in the PRO12.
He also got his first taste of European action when coming on as a replacement against French side Toulouse at the Sportsground. He made further appearances against Zebre and Heineken Cup semi-finalists Saracens.
The former St. Joseph's (the Bish) student has been recognised for his ability to kick long range penalties and playing for the Connacht Eagles in this season's British & Irish Cup, he landed a last-minute penalty kick from 60 metres to win the game, 27-25, against Rotherham Titans.
Australian-born prop Bealham, whose grandmother hails from Enniskillen, has also graduated to the senior squad after two years in the Academy.
The IRFU were alerted to the fact that he was Irish qualified and Bealham got a trial with the Ireland Under-20s before the 2012 Junior World Championship.
Keen to stay on in Ireland after that, he was given a trial with the Connacht Academy and impressed Carolan who said, 'it was no holds barred but he came through it well. He has a good understanding of the game and how he can affect it'.
Following a number of games for the Connacht Eagles and his Ulster Bank League club Corinthians RFC, the 23-year-old loosehead made the step up to the PRO12 last month.
He came on as a replacement in the bonus point wins over Zebre and Benetton Treviso and also got game-time at Ravenhill last weekend.
Meanwhile, Galway-born centre Finn has seen his hard work rewarded with a one-year senior contract after three years in the Connacht Academy.
Hailing from Ballinasloe, the 21-year-old captained Cistercian College Roscrea to the Leinster Schools Senior Cup final in 2011 where they lost out to Clongowes Wood College.
Playing his club rugby with Buccaneers, Finn has also represented Ireland at Under-19 and Under-20 levels. He was a regular starter with the Connacht Eagles in the British & Irish Cup and interpro games this season.