Due to the current financial situation at Fratton Park, the 23-year-old has joined the club on non-contract terms.
However, manager Michael Appleton is hoping that the move will turn into a permanent one.
"Obviously we need a goalkeeper and Simon has been playing in the pre-season games for us," Appleton told the club's official website.
"It's on a non-contract basis, so it could be ripped up at any time, but hopefully in the future we'll be looking at giving him a contract."
Eastwood has gone straight into the squad for this evening's League Cup tie against Plymouth Argyle.