Eastwood joined the club at the start of the season and has served primarily as an understudy to either Paul Robinson or Jake Kean.
However, he has played in nine Blackburn games and impressed when they kept a clean sheet away at QPR in December.
"I'm delighted," Eastwood told Blackburn's official website.
"It is a good achievement for myself to stay at a club like this, so I'm looking forward to the future.
"I'd like to think that when I got in the team I did a good job. Right now Robbo is playing really well but whenever I'm called upon I'm sure I'll be ready.
"There's me, Jake and Robbo training hard and pushing each other every single day. Everyone gets along with each other and we work well together, so it is good. I enjoy coming in every day."