It will see the Blues midfielder stay with the Sky Bet League One outfit until the end of the season.
Elliott initially joined the Robins at the end of January on an emergency loan until March 1. During his time at Ashton Gate, Elliott has made seven appearances for Steve Cotterill's side.
His most recent appearance came in Saturday's 2-1 home victory against Gillingham. The result saw Robins climb out of the relegation zone and go above Crewe Alexandra on a better goal difference.
Speaking about Elliott last week, Robins boss Cotterill said: "Wade is a model professional and is a very young 35 in terms of his fitness. He has a real energy about him and likes to put himself about.
"We've seen the real Wade after a couple of difficult games early on. I've already gone on record to say I threw him in too soon after not playing regular first team football since October. But we've seen what he is all about in the last few games and I want that for the rest of the season."
He added: "Wade has the qualities I look for in a player. He has a fantastic character and is a winner. It's that sort of mentality I wanted to get into the dressing room. He sets an example on and off the pitch and has been first-class since he walked through the door."