The 27-year-old scored 12 goals including a hat-trick in 45 appearances for Aldershot.
Reid played at Coventry City, Cheltenham, Grays Athletic, Newport County and Stevenage before joining the Shots.
Reid was delighted to join the Shrimpers: “I’m pleased to have signed a deal with Southend United and I can’t wait to get started. Last season was tough with everything that went on at Aldershot but I’m very happy to be back in the Football League with Southend and hopefully we can have a successful season.
“Hopefully I can score goals and show the fans what I can really do. I can’t wait for the season to get started against Plymouth on Saturday.”
Blues boss Brown added: “I’m delighted to have signed Craig. He’s scored goals at this level last season in a side battling relegation and was very prolific when he played for Newport County.
“Along with Freddy Eastwood and Barry Corr we’ve now got three strikers who have performed at a high level in this division and we’ve also got young Seedy Njie. Things are starting to come together and I’m very pleased Craig has decided to come to Roots Hall. He will give us something different up top and I’m sure he’ll do well for the Club.”