Hammersley has made 17 appearances in a breakthrough season this term.
“If someone had said to me that I would debut in the Premiership and the Champions Cup this year, then I would have bitten their hand off,” the winger said.
“I can’t wait to continue learning and growing with this group and hopefully contribute to more success at Sandy Park going forward.”
Chiefs director of rugby Rob Baxter was delighted to secure both players on new deals.
“Tommy at the start of the season was like a steam train,” Baxter said.
“He’s very strong on the ball and he was making numerous breaks from behind the line. He was very safe and very strong for us. He was tearing it up in the Premiership – leading the way in a number of charts.
“Ben is also part of a young and exciting group that have broken through this season. “Similar to Tommy, having got in the team he was playing exceptionally well – very strong on the ball, very strong defensively.”
Exeter have three league games remaining this season and sit seventh in the Premiership, five points off the top four play-off spots.