Bronze turned down a deal which would have made her City's highest earner to sign a three-year contract with Lyon.
The 25-year-old is a key part of the Lionesses side to reach consecutive semi-finals at major tournaments.
Germany international Bremer, 21, has won two Women's Champions League titles with Lyon in the last two seasons.
After winning back-to-back league titles with Liverpool Ladies, Bronze joined City in 2014 and was named as the PFA Women's Player of the Year for a second time in 2017.
The ex-Sunderland and Everton full-back is widely hailed as one of the best defenders in the world and has won the Women's Super League in 2016 as well as a Continental Cup (League Cup) and the 2017 Women's FA Cup with City.
She was also part of the side that lost 3-2 on aggregate to Lyon in the 2016-17 Champions League semi-finals, before the French side's victory over Paris St-Germain on penalties in June's final.
England right-back Lucy Bronze has joined Women's Champions League holders Lyon from Manchester City with forward Pauline Bremer moving the other way.