The 32-year-old Liverpool striker takes the armband after regular skipper Aaron Ramsey was ruled out of the game with an ankle injury.
It will mark the first time the 67-cap forward has led his country since the Euro 2012 qualifying defeat in Montenegro in September 2010, and could also prove to be his last game for Wales.
Bellamy was hit particularly hard by the death of manager Speed in November, and is known to be considering his international future, although new boss Chris Coleman is trying to convince him to play on through the 2014 World Cup qualifiers.
Coach Osian Roberts said: "For obvious reasons, Craig will lead the side tomorrow night.
"He knew Gary better than anybody, he is a close friend of the Speed family and it seems only right that he should lead Wales on the night."
Coleman also praised vice captain Ashley Williams, after the Swansea defender allowed Bellamy to take the armband on what will be an emotionally-charged occasion.
"It is a real nice gesture from Ashley Williams," he said. "I spoke with Ashley yesterday, and it's a different game, there is no getting around it.
"It's a friendly building to the big one against Belgium in September, but there is a different slant on the game for obvious reasons.
"It is fitting. Aaron is our captain and he will be leading the team out with Gary's two sons, Tom and Ed, and Craig is captain on the night, which is right thing to to and it is also a nice gesture from Ashley Williams."
But Coleman says he is still unsure as to whether Bellamy, who was due to appear at a press conference alongside the manager, Roberts and Ramsey but was a late withdrawal, will extend his Wales career beyond Wednesday night.
"I don't want to sit here and say what I think is going to happen because I would prefer the words to come from Craig," he said.
"He is an experienced player, a passionate Welshman and he still has lots to offer.
"It will be down to whatever Craig wants to do.
"I hope he stays as we need a Craig Bellamy on and off the park. He is a winner who wants things done right.
"I hope Craig stays and I will do my best to keep Craig and we are a better team and squad with him about.
"I hope whatever decision he makes is a good one, and I am confident and hopeful it will be a good one, but it's up to Craig to come out and say that."
With Ramsey already ruled out, Wales were dealt another blow after first-choice goalkeeper Wayne Hennessey was forced to withdraw with a sore ankle.
The Wolves keeper's absence, and the Achilles injury Boaz Myhill is suffering from, means Crystal Palace's Lewis Price or Aberdeen's Jason Brown could be in line to start.