That total has worked him into third place in the PRO12 all-time try scoring list level with Nikki Walker and just behind Shane Horgan (39) and Tommy Bowe (46).
Visser picked up 15 out of a possible 28 votes for the two wing positions, with his nearest rivals way back on four.
There are five players in the 2011/12 RaboDirect PRO12 Dream Team who have retained their place from the previous year.
A panel of 14 journalists from Ireland, Italy, Scotland and Wales were canvassed to select the team after 19 rounds of the tournament and four of the returning players were in the back-line.
Leinster's skilful utility back Isa Nacewa once again won the full-back shirt, beating off the strong challenge of Glasgow Warriors rising star Stuart Hogg, while Ruan Pienaar was the overwhelming choice at scrum half with 10 of the 14 votes.
Cardiff Blues centre Casey Laulala was the other player to make it two in-a-row as he won the race to join the Ospreys' Ashley Beck (8 votes) at centre.
His Blues team-mate, Wales Grand Slam winger Alex Cuthbert, took the left wing spot on try count over Munster's Simon Zebo.
It was also tight at out-half where Glasgow Warriors' Duncan Weir just pipped Leinster's Ian Madigan for the number 10 jersey after both players received four votes. In the end, Weir's superior scoring record earned him the half-back berth alongside Pienaar.
Only one forward survived from the 2010/11 Dream Team, Leinster hooker Richardt Strauss. He polled eight votes with the Ospreys' Richard Hibbard his nearest rival with three.
There was another close call at loosehead prop where Glasgow's Jon Welsh and Leinster's Heinke van der Merwe were locked on three votes each. In the end, the decision went to Welsh on the basis he had scored three tries to van der Merwe's one.
Munster's BJ Botha beat off the challenge of the Ospreys' Adam Jones and Ulster's John Afoa to complete the front row as the tighthead choice.
There were 15 different players put forward for the two second row positions, but Ulster's Dan Tuohy and Glasgow's Tom Ryder were the clear favourites over some illustrious candidates.
Tuohy topped the poll with six votes, while Ryder had four, and their elevation into the Dream Team was a reflection on their reliability and durability at the heart of their respective packs over the season.
The back row comprises three players who failed to make their nation's World Cup squads, yet all featured in the RBS 6 Nations.
Edinburgh's Dave Denton took the blindside flanker position ahead of nine other candidates, while new England number 8 Ben Morgan of the Scarlets crowned his great season by polling twice as many votes as his nearest rival.
The number 7 jersey went to the Ospreys' outstanding openside flanker Justin Tipuric, who received the third highest number of votes of any player - behind Pienaar (10) and Visser (15) - with nine to leave the 2011 nominee, Sam Warburton, trailing in his wake.
No fewer than 89 players from all 12 sides in the RaboDirect PRO12 received votes and the final make-up of the team is as follows:
2011/12 RABODIRECT PRO12 DREAM TEAM:
15 - Isa Nacewa (Leinster)
14 - Tim Visser (Edinburgh)
13 - Casey Laulala (Cardiff Blues)
12 - Ashley Beck (Ospreys)
11 - Alex Cuthbert (Cardiff Blues)
10 - Duncan Weir (Glasgow Warriors)
9 - Ruan Pienaar (Ulster)
1 - Jon Welsh (Glasgow Warriors)
2 - Richardt Strauss (Leinster)
3 - BJ Botha (Munster)
4 - Dan Tuohy (Ulster)
5 - Tom Ryder (Glasgow Warriors)
6 - Dave Denton (Edinburgh)
7 - Justin Tipuric (Ospreys)
8 - Ben Morgan (Scarlets)
Teams (8): Glasgow Warriors 3, Cardiff Blues 2, Edinburgh 2, Leinster 2, Ospreys 2, Ulster 2, Munster 1 and Scarlets 1
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