The 27-year old right-back has joined the Ibrox club on a two-year deal after leaving English side Bristol City.
Foster spent time on loan with 'Gers in 2010-11 whilst with Aberdeen and will now head back to Ibrox on a permanent basis.
"The fans here expect a certain level of performance and expect to win every game. Hopefully I can bring something to the team in that respect," he told RangersTV.
"When I first came down here from Aberdeen the last time, I did get my eyes opened a bit and I realised just how big the club was.
"Now, already knowing what the fans are like and everything else too, I understand what to expect.
"The league is the most is the most important thing for us this season but the cups are massive for us too.
"We want to see how well-equipped we are against the bigger teams and last year was a bit disappointing in that respect so we'll be looking to do better this year."