Terry went on to confirm the deal on Wednesday, saying "it's official," via Mark Berman of Fox 26.
There had been rumblings recently that Terry was nearing a deal to remain in Houston, and it's not hard to understand why the team wanted to keep the veteran guard.
The Rockets got Terry from the Sacramento Kings in a trade for Alonzo Gee last September. He played an integral role off the bench during Houston's run to the Western Conference Finals. The 37-year-old averaged seven points per game and shot 39 percent from three-point range in 2014-15.
There haven't been many bench players better than Terry since 2007-08, when the Dallas Mavericks started using him in that role. He was named the NBA's Sixth Man of the Year in 2008-09 and continues to shoot a high percentage from distance.
The balance of power in the NBA lies in the Western Conference. Houston owned the second-best record in the conference last year at 56-26 and is now set up for another big season in 2015-16 after taking care of its starting lineup and bench.