Central defender Tate is highly-rated by the coaching staff at Old Trafford and was named The Red Devils' Young Player of the Year for the 2000/01 campaign.
The 19-year-old has yet to make his first team bow, although he was an unused substitute when United's second string lost 4-0 at Arsenal in the third round of the Worthington Cup last month.
Wood is an 18-year-old striker, who is also waiting in the wings for an opportunity to demonstrate his worth at the Theatre of Dreams, and the temporary switch to the Jupiler League strugglers should enhance his prospects of making a breakthrough.
United have enjoyed a fruitful relationship with Antwerp during recent seasons with the likes of Ronnie Wallwork, John O'Shea and Luke Chadwick all savouring spells at the De Bosuil Stadium before forcing their way into manager Sir Alex Ferguson's plans.
Antwerp have announced the moves on their official website, although United told planetfootball.com that the deal has not yet been completed.
