Coverage will start on Saturday at 6.00pm, with the match kicking off at 6.15pm. The programme will be presented by Calum Macaulay with commentary from Hugh Dan MacLennan and analysis from former Scotland international and British Lion John Beattie.
The clash will see reigning champions Leinster who finished top of the standings during the regular season host Glasgow Warriors who were second in the campaign and are making their inaugural appearance in a PRO12 final.
Meanwhile, Glasgow Warriors have also confirmed that supporters who can't travel to Dublin for the final can watch the game on a big screen in Merchant Square in Glasgow.
There will also be a Fan Zone at the Ballsbridge Hotel in Dublin from 12 noon for supporters going to the game.
Scottish Rugby's director of commercial operations, communications and public affairs Dominic McKay said: "This will be an historic occasion for Glasgow Warriors and Scottish rugby and we're delighted the game will be shown live on BBC ALBA and BBC TWO Scotland on Saturday.
"BBC ALBA have screened the majority of Glasgow's games this season on their way to the final and are big supporters of Scottish rugby.
"It's fantastic that even more people will get to watch the final on Saturday evening and we'd like to thank BBC ALBA and BBC Scotland for showing the game live.
"Everyone at Scottish Rugby would like to wish the Warriors all the very best in the final.
Glasgow Warriors managing director Nathan Bombrys added: "It is great news for our supporters that the final will be on both channels.
"With the game also being shown live in Merchant Square, it means supporters can watch the game together in the centre of Glasgow, while fans travelling to Dublin will be able to enjoy our pre-match Fan Zone close to the stadium.
"We're expecting the largest number of television viewers for a Glasgow Warriors RaboDirect PRO12 game.
Head of content for BBC ALBA Alan Esslemont said: "We are delighted to be bringing viewers a fantastic live package from Saturday's RaboDirect PRO12 final as Glasgow travel to Dublin to take on Leinster.
"BBC ALBA's coverage this season has been very well received and we are looking forward to Saturday's game with much anticipation for Glasgow.
"It will be the exact same programme output from BBC ALBA that will be screened live on BBC TWO, allowing a greater fan base to enjoy our production and the live action as it happens.