The 26-year-old has become the club's fifth close-season capture in the process following earlier deals to bring in fellow wing-back Peter Kioso, central defender Jamie McCart and forwards Tom Eaves and Conor Washington.
Crewe-born Bramall, a pacey option on the left, was plucked from obscurity in 2017 when Arsenal took him from Northern Premier League club Hednesford Town and then loaned him and Carl Jenkinson to Birmingham City.
He left Arsenal in August 2019 to sign for League Two outfit Colchester United where he made 57 appearances before securing a mover to League One side Lincoln in early 2021.
Rotherham have reportedly triggered the £200,000 release clause in the contract of Bramall, who had a year remaining on his Imps deal. He has signed a three-year contract.