All three players can return from the list at any time, once they are medically cleared to play. The team didn't release any details on their injuries.
To make room for Hill on the roster, the Jets parted ways with kicker Andrew Furney.
"I'm extremely excited to be a part of the Minnesota Vikings moving forward," Walsh said. "I'd like to thank Rick Spielman, the Wilf family, Coach Zimmer, Coach Priefer and Rob Brzezinski for giving me this opportunity. I'm proud to be able to stay with the team that drafted me coming out of college and I look forward to what is in store for the future of this organization."
Gostkowski was slated to play the 2015 season under the franchise tag. He would have made $4.126 million. The two sides agreed to the contract before the 4 p.m. deadline Wednesday for players under the franchise tag to negotiate long-term deals this year.
The 31-year-old Gostkowski is a three-time Pro Bowler, including the last two seasons. He led the NFL in most points scored in 2008, 2012, 2013 and 2014. He is eighth on the active scoring list with 1,179 points, according to Pro-Football-Reference.com.
He has converted 86.8 percent of his field goals in his nine-year career -- all with the Patriots. He has missed just one extra point (450 of 451) in the regular season, with his only miss coming as a rookie in 2006.
Sturgis will miss the rest of the team's OTA sessions with the injury, reports the Miami Herald. Sturgis was 29-of-37 on field goals last season, and just 9-of-16 from beyond 40 yards.
Bogotay was a tryout player at rookie minicamp and previously a member of the Browns' practice squad. Gottschalk was with the Chiefs' practice squad last season.
"Am I thrilled about it? No, I don't think any other kicker is," Prater said in an interview with ESPN.com. "You know, they make these rules and they never talk to any of us about it. I don't know. I just feel that eventually they are just trying to weed kicking out of the game completely. It's something we'll have to deal with and hopefully make them all."
He also questioned the motive from the league with making this kind of rule change.
"I don't know what the owners and (NFL commissioner Roger) Goodell and all them are thinking," Prater said. "But I'm just going to try and do my job and keep my mouth shut for the most part."