Madigan landed four from five kicks at goal in Leinster's bonus-point win over Zebre but the 23-year-old has been overlooked in favour of his 21-year-old rival.
Jackson, who skippered Ireland at U20 level, started the Heineken Cup Final last term and has been a regular for Ulster since the departure of Ian Humphreys to London Irish. He has had to play second fiddle to Springbok scrum-half Ruan Pienaar when it comes to place kicking, however, and remains uncapped at international level.
Jonathan Sexton's hamstring injury means O'Gara is almost certain to start at fly-half in Edinburgh despite an uncharacteristically sloppy showing in Munster's defeat to the Scarlets on Saturday night, with Jackson awaiting his debut from the bench.
O'Gara missed missed three shots at goal - including a sitter from straight in front of the posts and just 25 metres out - as a lacklustre Munster failed to find the win that would have seen them move back into the RaboDirect PRO12 play-off places.
Ireland head coach Declan Kidney has named a total of 29 players in his squad for the Round 3 fixture but that number will be increased to 30 if Connacht centre Dave McSharry gets the all clear from a back strain that forced him to miss Friday's 22-10 defeat of the Ospreys.
The foot injury that has ruled Gordon D'Arcy out of the remainder of the tournament has left Kidney with a midfield headache, although he isn't short of options for a partner to Lions legend Brian O'Driscoll.
Luke Marshall, Fergus McFadden, Luke Fitzgerald or McSharry could start at inside centre against the Scots, or Kidney could move O'Driscoll to the No12 shirt and pick Keith Earls or Darren Cave outside the Leinster veteran.
Double Lions tourist Donncha O'Callaghan looks set to start in the second row after injury to Mike McCarthy, with Ulster's Iain Henderson and Lewis Stevenson and Leinster's Devin Toner competing for an extra forward position on the bench.
Simon Zebo's broken foot has left a wing berth wide open for the likes of McFadden, Earls or Fitzgerald, but there is still no place in the squad for Andrew Trimble.
Ulster's Australian-born loosehead Tom Court has been called up to replace the suspended Cian Healy but Munster's David Kilcoyne is expected to win the starting No1 shirt.
Ireland squad to meet at Carton House on Monday evening
Rory Best (Ulster), Darren Cave (Ulster), Tom Court (Ulster), Seán Cronin (Leinster), James Coughlan (Munster), Keith Earls (Munster), Luke Fitzgerald (Leinster), Declan Fitzpatrick (Ulster), Craig Gilroy (Ulster), Robin Henshaw (Connacht), Jamie Heaslip (Leinster), Ian Henderson (Ulster), Chris Henry (Ulster), Paddy Jackson (Ulster), Rob Kearney (Leinster), David Kilcoyne (Munster), Luke Marshall (Ulster), Fergus McFadden (Leinster), Conor Murray (Munster), Seán O'Brien (Leinster), Donncha O'Callaghan (Munster), Brian O'Driscoll (Leinster), Ronan O'Gara (Munster, right), Peter O'Mahony (Munster), Eoin Reddan (Leinster), Mike Ross (Leinster), Donnacha Ryan (Munster), Lewis Stevenson (Ulster), Devin Toner (Leinster)