Robinson, who became a free agent when his contract expired at the end of the recent campaign, progressed through the ranks with the Seagulls' youth set-up and made over 120 appearances for the League One outfit.
The 22-year-old also enjoyed two separate loan spells with Aldershot where he made over 30 appearances and Shrewsbury manager Paul Simpson told the club's official website: "I'm delighted that we've been able to get Jake Robinson to sign for the club. He's a player who I have liked for a number of years and kept an eye on how he's been developing.
"He's a young lad who got into the Brighton side at a very young age, played a number of games for them and did very well. He was always thought of as a bright young player but just seemed to lose his way a little bit and fell out of favour.
"I thought he did well when he came on against us in the JPT [Johnstone's Paint Trophy] game here last season and I tried to bring him in before the loan window closed but we couldn't manage to do that.
"He then went out to Aldershot and did very well and got to know this league well."