The Rockies are set to pay $500,000 of Street's $7.5 million contract in 2012 and could pay the same amount in 2013 if the Padres don't exercise their half of his mutual option.
Street's option for 2013 is $9 million with a $500,000 buyout.
"He's a very proven closer, has done it in this division and he's had three good years with Colorado, which is a hard place to pitch," said Padres general manager Josh Byrnes.
"And he has got the moxie for the back end. A lot of ingredients we liked. We're happy how it ended up."
Street, 28, had 29 saves in 33 opportunities last season with the Rockies and had a 3.86 ERA. He has a career record of 30-21 over parts of seven Major League seasons with a 3.11 ERA and 178 saves.
Street has been very successful at Petco Park, where he hasn't allowed an earned run in 11 1/3 innings, with 17 strikeouts and five hits allowed.
"He can make pitches; he's not a velocity guy but he can really command," Byrnes said. "He doesn't beat himself."
Street allowed a career-high 10 home runs last season, but Byrnes is hoping a change of venues to an extreme pitchers' ballpark (Petco Park) will help.
"It won't be tough at all. ... As a pitcher, everyone likes pitching at sea level rather than 5,000 feet," Street said. "Petco is known as a pitchers' park and I feel like I've had some success there.
"But I expect results [even] if I was pitching on the moon."
The Padres came to the Winter Meetings looking to address the back end of their bullpen, as news of Bell's three-year deal with the Marlins for $27 million (with a vested option for a fourth year) came to light at the end of last week.
Finding a closer wasn't a singular focus for the Padres this week but it was pretty close.
"It was time to go," Byrnes said.
Byrnes said that he has been talking with the Rockies for close to a month and cited his relationship with Rockies general manager Dan O'Dowd. Byrnes was the assistant GM with the Rockies for two seasons.
The Minor League player headed to the Rockies isn't regarded as a prospect.
Street was the American League Rookie of the Year with the Athletics in 2005. He joined the Rockies before the '09 season, along with outfielder Carlos Gonzalez and left-handed pitcher Greg Smith, in the deal that sent outfielder Matt Holliday to Oakland.
In '09, Street converted 35 of 37 save opportunities, but suffered from arm soreness at the end of the year. He had a blown save and a loss in the Rockies' heartbreaking three-games-to-one loss to the Phillies in the National League Division Series.
After the season, the Rockies signed him to his current three-year, $22.5 million contract.
In 2010, Street began the season on the disabled list with a shoulder issue, sustained a groin injury during a rehab assignment and wound up missing the first 69 games. After returning, he converted 20 of 25 save chances.
Last season, a bout with biceps tendinitis in August forced Street to the disabled list and opened the door for Rafael Betancourt, who finished the year 8-for-9 in save chances.
"I loved my time in Denver," Street said by telephone Wednesday. "I was always treated first class. I enjoyed my time there. I'm going to miss my teammates and coaches. But I think that's the way it should be.
"But now I'm going to give that love to the Padres organization."
Byrnes said earlier this week that he was unwilling to go more than two years on a new deal with any pitcher, starter or reliever.
Street will certainly have big shoes to fill in replacing Bell, who has more saves than any other pitcher since the start of the 2009 season.
San Diego will receive two additional Draft picks for offering Bell arbitration now that he has signed with the Marlins.
To make room for Street on the 40-man roster, the Padres designated outfielder Jeremy Hermida for assignment Wednesday.