The midfielder spent much of pre-season in training with Rovers and played in the friendlies against Bradford City, Wakefield AFC, Newcastle United, Sheffield United and Harrogate Town.
He was informed this week that Rovers would not be offering him a contract and secured a deal with Swindon, who are beginning a rebuild under new ownership.
Rovers boss Richie Wellens changed his mind on several occasions in the last few weeks over his intentions for Reed.
Initially he believed Reed was too similar in skillset to the other midfielders on his books and would not provide the physicality in the middle of the park he was searching for.
Strong performances from the 24-year-old through pre-season saw Wellens come around to the idea of putting him into the heart of a highly technical midfield and chasing a more defensively strong player in future windows when finances were freed up.
His hopes of getting fringe and young players out on loan have yet to be realised, meaning little funds are currently available from the playing budget.
Barnsley-born Reed has made 190 senior appearances and was involved in Peterborough United’s promotion to the Championship earlier this year, meaning he rightly commands a good wage.
It became clear that Rovers would not be able to offer him an acceptable deal before the start of the season, and on being informed that was the case, Reed explored other options, leading him to the County Ground.
It is understood Rovers will confirm the signing of one of the crop of trialists of which Reed was a part.
Meanwhile, former Rovers loanee Matt Smith has joined Hull City on a season-long loan from Manchester City.