The 20-year-old New Zealand striker had been on loan with Birmingham from West Brom for the last six months but returned to The Hawthorns after that loan deal expired last week.
Blues boss Chris Hughton had been keen on bringing Wood back to St Andrews on a further loan deal but the player has instead joined Bristol City on loan for the remainder of the season.
Wood had scored ten goals in 27 appearances for Blues this season.
Robins boss Derek McInnes told his club's official website: "Chris is someone I have been aware of for some time and I tried to sign him on a couple of occasions at St Johnstone.
"In the end he went to Barnsley and Brighton due to restrictions on cross-border loans.
"I'm delighted we've been able to add him to our squad for the rest of the season and he will be a real asset.
"He's a big lad with good feet and he's already shown himself to be a proven goalscorer at Championship level.
"I'm sure he will prove a valuable addition to the squad. I've seen him play a number of times; he's young and hungry and I'm sure he will enjoy his time with us."