The move will allow an extra 10,000 fans to see the games, which Bristol head coach Richard Hill believes will be of huge benefit to his side.
"Playing at Ashton Gate is no problem and I expect it to make these two fixtures even bigger than they would have been at The Mem," said Hill.
"Last year, our fans were magnificent in the early-season win against Bath - packing more Bristol fans into Ashton Gate will raise the temperature a few degrees more for our neighbours.
"I expect them to lift us in the same way for the Tigers game too."
Bristol set a then-Premiership attendance record at Ashton Gate, home of football neighbours Bristol City, for their 30-20 victory over Bath in May 2003.