The former Dutch international made 22 appearances for the Mariners, scoring twice but has decided not to stay under new coach Mike Mulvey.
Twente, who are one of the bigger mid-table clubs in the Netherlands, finished 18th last season and will play in the Eerste Divisie. Brama won the Eredivisie title and KNVB Cup with Twente in 2010 and 2011 respectively.
"That we are playing in the first division next season is a weakness, but that did not play a role, so we have to get the club up again," Brama told the Twente club website.