The contract is through the 2020 season with a club option for 2021, general manager A.J. Preller announced. The deal is reportedly worth $19.75 million.
Hand, 27, went 3-4 with 21 saves and a 2.16 ERA last season. He's been mentioned in trade talks since last summer.
"I'm 27 right now and have the chance to be a free agent again at a younger age, which is something we kind of wanted to keep in play," Hand said. "I don't think they're far off here from winning -- maybe three or four years from now will be a very exciting time."
The Padres are heading into the second year of a deep rebuild. They hope to be competitive by next season.
The Padres signed Hand off waivers from the Marlins on April 8, 2016.
"Brad's a guy that's going to lead the bullpen and anchor the bullpen," manager Andy Green said. "He has the skill and the makeup to do those things. Resiliency, too. I've never been around a pitcher that takes the ball as willingly and as often as he does. He wants to be on the mound every single day. He loves to pitch."