Eastwood has been training with the south coast club for the past month and featured in friendlies against Gibraltar, Bolton and AFC Wimbledon.
The 23-year-old is eligible to go straight into the team to face Plymouth in their Capital One Cup first-round tie.
Pompey are expected to field a youth team in the game with Eastwood and assistant manager Ashley Westwood the only exceptions.
Blues boss Michael Appleton told the club's official website: "Obviously we need a goalkeeper and Simon has been playing in the pre-season games for us.
"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."