One Direction star Tomlinson and former Rovers chairman John Ryan's bid to buy the League One side collapsed on Thursday when it was rejected by the Football League.
Rovers will therefore remain in the hands of major shareholders Dick Watson and Bramall, who has vowed to back manager Paul Dickov in the transfer market as they aim for promotion back to the Championship.
"It was with reluctance we agreed to the takeover simply because we have been pleased with the journey the club has made since our time as owners both on and off the field," Bramall said in a statement on the club's official website.
"However John and Louis both have a clear passion for the club and we did not want to stand in their way.
"Our primary motive throughout the negotiations has been to secure the future of Doncaster Rovers and to ensure the club is in a position to thrive both on and off the field while protecting the future of all staff.
"Hence why we agreed to write off our loans to the club as part of the proposed takeover agreement
"While we did not expect to be in this position, the opportunity that has presented itself is one that is welcomed with a positive attitude.
"We are looking forward to working with Paul Dickov, Gavin Baldwin and the rest of the senior management team and they of course will have our full support.
"We appreciate the difficult situation Paul has found himself in through no fault of his own.
"The delay in transfer activity has of course had short term impact on our season preparations but we are hopeful as a board we can support Paul with a playing budget that allows him to achieve all of our ambitions for a return to the Championship."
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