Striker Asante could make his League One debut for the Shrews in Friday's game at Carlisle.
The 20-year-old made his first-team bow for the Blues during last season's Europa League home game against Nacional.
He has also had a previous loan spell with Northampton at the end of December 2011 when he made four appearances and scored one goal.
Central defender Deaman, 19, who joined the Blues in the summer of 2011 from Wrexham's academy, trained with his new Cheltenham team-mates on Thursday and is available to face Port Vale on Friday.
"I've known Jack for a couple of years and he is a good player and athlete," Town manager Mark Yates told the club's official website.
"We need to cover every eventuality and we are a little light in defence so Jack will give us some protection. He knows what to expect here and he is ready to try and prove himself."
Cheltenham had earlier also extended the loan stay of Reading centre-back Michael Hector, 20, until the end of the season.