Walsh made his debut as a late replacement in last weekend's home win over Zebre, while Joyce's previous appearance was in the derby defeat to Leinster in December 2011.
The side will be captained by tighthead prop John Afoa, who is joined in an all-new front row by Nigel Brady and Callum Black.
Dan Tuohy and Neil McComb come in to the second row in place of regular skipper Johann Muller and Lewis Stevenson.
Robbie Diack, the only forward retained from the Zebre fixture, starts again at number 8 and will combine in the back row with Joyce and Ali Birch.
With Paddy Jackson making his debut for Ireland this weekend, Mark Anscombe has called upon Paddy Wallace to direct affairs from out-half.
The back-line reshuffle also results in Andrew Trimble moving to outside centre where he is partnered in midfield by Ireland Under-20 international Stuart Olding, who produced an impressive performance off the bench last Friday.
Michael Allen will line up on the right wing for his 12th cap, with Walsh on the opposite flank. Ruan Pienaar (scrum half) and Ricky Andrew (full-back) complete the backline.
Andrew Warwick again has an opportunity to earn his first cap after being named among the replacements for the second time this season.
Rob Herring, Ricky Lutton, Alan O'Connor and Mike McComish are the other reserve forwards. Paul Marshall, Darren Cave and Chris Cochrane are the back-line options and should provide some spark if called upon.
ULSTER (v Glasgow Warriors): Ricky Andrew, Michael Allen, Andrew Trimble, Stuart Olding, Neil Walsh; Paddy Wallace, Ruan Pienaar; Callum Black, Nigel Brady, John Afoa (capt), Neil McComb, Dan Tuohy, Conor Joyce, Ali Birch, Robbie Diack.
Replacements: Rob Herring, Ricky Lutton, Andrew Warwick, Alan O'Connor, Mike McComish, Paul Marshall, Darren Cave, Chris Cochrane.