"Oh man what a time.... To be alive," Anderson tweeted after signing the offer sheet.
Alonso sat out the 2014 season after tearing his ACL,Jerseys NBA Cheap China, hurt the same knee again last year and started only one game for the Eagles.
"It's definitely all behind me," Alonso said. "I feel great. I don't make excuses on my knee. I didn't play very well, but that's how it goes, and I just try to get better. But I feel great."
The Dolphins signed tackle Jermon Bushrod, a nine-year veteran who started four games last season for the Bears, where Gase was the offensive coordinator.
Anderson, undrafted out of Cal in 2013, rushed for 90 yards and one touchdown in the Broncos' 24-10 win over the Carolina Panthers in the Super Bowl. He chose Miami to make his first free agent visit.
"The issue was the physical," he said. "Everything is good now. I passed physicals both with Miami and Philadelphia, so I'm ready to go."

He and Maxwell both said they'll be ready for minicamp in May.
In addition to Miller, they lost defensive end Olivier Vernon, cornerback Brent Grimes and receiver Rishard Matthews.
Anderson rushed for 720 yards last season for the NFL champion Denver Broncos, who have five days to match the offer. They're considered unlikely to do so.
Maxwell said he passed two physicals before the trade that sent him and Alonso to Miami from the Philadelphia Eagles was finalized. Maxwell missed the final two games last season with a shoulder sprain, and he acknowledged his health was a concern before the Dolphins approved the deal.
As if to underscore his point, Maxwell was 15 minutes late for a conference call with reporters because he was working out.
MIAMI (AP) — Now that C.J. Anderson's a Super Bowl-winning running back,Cheap Jerseys From China, the Miami Dolphins want to give him the ball.
The restricted free agent signed an $18 million,Wholesale NFL Jerseys Authentic, four-year offer sheet Thursday with Miami.
Miami also signed linebacker James-Michael Johnson and center-guard Jacques McClendon. Earlier this week they added defensive end Mario Williams, cornerback Byron Maxwell, linebacker Kiko Alonso,Wholesale Jerseys USA, safety Isa Abdul-Quddus and tackle Sam Young.
"You can probably Google it and find out," he said.
Maxwell signed a $63 million,Jerseys China Cheap NFL, six-year contract to join the Eagles a year ago. He said he agreed to restructure that deal with the Dolphins, but declined to give details.
New Dolphins coach Adam Gase needs a replacement for running back Lamar Miller, who signed a free agent deal with Houston. Gase was offensive coordinator for the Broncos and Anderson in 2013-14.