Elneny, who joined Arsenal from Basel in January, has made just one appearance in the league for the Gunners this term, having featured for 20 minutes against Manchester United this week.
Meanwhile, Welbeck, who only recently returned to action following a lengthy injury, makes his second start of the campaign and has featured in each of his side's last three matches - scoring two goals.
The two line up in Saturday's crucial clash against Tottenham together, with Welbeck replacing Giroud and Elneny taking the place of Joel Campbell, and are two of four changes Arsene Wenger has made for the match at White Hart Lane.
David Ospina has come in to replace the injured Petr Cech, while Kieran Gibbs, who has not started since late December, has taken the place of Nacho Monreal.
Tottenham, meanwhile, have also made four changes, with Kyle Walker, Danny Rose, Mousa Dembele and Dele Alli returning to the first team as Kieran Trippier, Ben Davies, Ryan Mason and Nacer Chadli all drop to the bench.
Spurs sit three points ahead of their north London rivals ahead of Saturday's game, which could have a pivotal role in this season's title race.
TOTTENHAM: Lloris; Walker, Alderweireld, Wimmer, Rose; Dembele, Dier; Lamela, Eriksen, Alli; Kane.
Subs: Vorm, Davies, Trippier, Carroll, Chadli, Mason, Son.
ARSENAL: Ospina; Bellerin, Mertesacker, Gabriel, Gibbs; Coquelin, Elneny; Ramsey, Ozil Sanchez; Welbeck.
Subs: Macey, Chambers, Monreal, Flamini, Campbell, Walcott, Giroud.