The attacking duo will play in the FA Cup third-round replay and increase the options open to the boss at a busy time for the club.
Rooney has been out since the draw at Swansea before Christmas while Nani's last appearance was 15 games ago in Braga. Sir Alex also hinted that Javier Hernandez and Antonio Valencia appear primed to complete the front-four positions.
"Both [Rooney and Nani] will play," confirmed the boss to MUTV. "Both are fit.
"[There's] Chicha and Antonio, we've got a strong squad, you know. There won't be many changes really. Wayne coming back is good news. He's been training for a week and looking good. As for Nani, he came back from his spell abroad [having a break in Dubai] and is really looking very good. So I'm fine and will play a strong team."
The manager, whose celebration at Upton Park after Robin van Persie's last-gasp leveller left no doubts as to his passion for the competition, feels United are overdue a good cup run after last lifting the trophy back in 2004.
"Of course, we've got a big squad but it's also an important tie tomorrow for the club," he asserted. "We want to try and have a go at this FA Cup.
"We haven't had a run for a long time, two or three years, as we had some bad draws of course. We're at home and we have got to take advantage of that. If we get through, we have got another home tie [against Blackpool or Fulham] so there's a big incentive for the club to make sure we get through."