The Ulster back row has been rewarded by Farrell after making an impact off the bench in the games against France, Italy and England.
Timoney, 30, is one of two changes to the back row as Jack Conan is recalled after he missed the emphatic win over England at Allianz Stadium because of illness, meaning Tadhg Beirne shifts to the second row.
Farrell has also made two changes to the front row with Ulster's Tom O'Toole replacing the injured Jeremy Loughman at loose-head prop and Ronan Kelleher recalled at hooker.
In the only change to the backline, Jacob Stockdale replaces the injured James Lowe on the left wing.
Stockdale started Ireland's defeat by France in Paris at full-back, but despite Tommy O'Brien's excellent performance off the bench against England, Farrell has given the 2018 player of the tournament another chance to nail down a starting berth.
Timoney to make first Six Nations start for Ireland - follow live
Timoney happy he didn't give up on Ireland dream
In contrast, there were no Ulster players in Ireland's matchday squad for the 27-18 win over Wales in Cardiff last year.
Doak is set to win his first cap as scrum-half cover for Jamison Gibson-Park - who will make his 50th Ireland appearance - while hooker Stewart will make his Six Nations debut.
"We have two special milestones in the squad this week at opposite ends of the scrum-half spectrum," said Farrell.
"I would firstly like to congratulate Nathan on his first international selection. Nathan has been around a few Ireland camps in recent years and has impressed with the consistency and quality of his play in training and with Ulster over a longer period.
"I know how much this means to Nathan and we are determined to make this a special few days for him and his family."
Watch on iPlayerListen on SoundsListen on Sounds, BBC Radio Wales, BBC Radio Cymru and BBC Radio Ulster. Watch on S4C.
Munster centre Tom Farrell is also set to make his Six Nations debut off the bench with Bundee Aki not included despite returning from a four-game ban for verbally abusing a referee.
Joe McCarthy and Josh van der Flier drop to the bench while Dan Sheehan is not included.
Wales named their team earlier on Wednesday with wing Ellis Mee recalled as one of three changes made by head coach Steve Tandy.
Ireland have won the past four Six Nations meetings with Wales and have not lost to this fixture at home since 2012.
Victory on Friday will keep alive Ireland's title hopes and set up a Triple Crown decider with Scotland in Dublin on 14 March.
Ireland: Osborne; Baloucoune, Ringrose, McCloskey, Stockdale; Crowley, Gibson-Park; O'Toole, Kelleher, Furlong, Ryan, Beirne, Conan, Timoney, Doris (capt).
Replacements: Stewart, Milne, Clarkson, McCarthy, Van der Flier, Doak, Farrell, Frawley.
Wales: Rees-Zammit; Mee, James, Hawkins, Adams; Edwards, T Williams; Carre, Lake (capt), Francis, D Jenkins, Carter, Mann, Botham, Wainwright.
Replacements: Elias, Smith, Griffin, Beard, Cracknell, Hardy, J Evans, Hennessey.
