He will now link up with former manager Joe Royle, whom he played under at Ipswich, and could pen a permanent deal at Boundary Park in the summer.
The 25-year-old joins Alex Russell and Lloyd Owusu in having moved away from Cheltenham in the past month, while Ashley Vincent's switch to Colchester is also set to go through soon.
But unlike the others three deals, chairman Paul Baker insists Westlake's departure was not a case of lightening the wage bill at the cash-strapped club or raising funds.
"Neither the club nor manager Martin Allen wanted Ian to leave," Baker told Cheltenham's official website. "While the move will of course help our current financial position, this was not the main factor in reaching our decision. It was Ian's desire to leave and we have parted very amicably."