Rovers had been at Azimghur Barracks in Wiltshire after leaving their former HQ in Golden Hill, Horfield during Ray Graydon's spell in charge.
"It's about perception - we're back in Bristol," Rovers chairman Nick Higgs told BBC Points West.
"It's also about the facilities here, which are fantastic."
He added: "We've got a training pitch that has been marked out exactly to the same size as the Memorial Ground."
£3m has been spent on the centre at Knowle that the team will now be using.
"The facility was good at Colerne," boss Paul Trollope told BBC Points West. "But in the winter months it was especially harsh out there with the wind and the rain.
"It was a 30-40 minute journey before and after training, so the shorter journey time does make a difference to the players' rest and recovery.
"All round it's a great thing for us."