The team announced the signing on Sunday. Multiple reports say it is a three-year, $19.5 million deal.
The Blues dealt Stastny, 31, to the Jets at the trade deadline this past season for prospect Erik Foley and first- and fourth-round draft picks.
Stastny had 13 points in 19 regular-season games, but he was a big contributor in the playoffs, with 15 points in 17 games.
He finished a four-year, $28 million deal that he had signed with St. Louis.
Stastny's most productive years came with Colorado at the beginning of his career. He had 78 points in his rookie season in 2006-07 and a career-high 79 in 2009-10. He made his only All-Star Game in 2011.
The Knights also re-signed power forward Ryan Reaves. Vegas acquired him from Pittsburgh at the trade deadline to add size and grit to a speedy lineup. He had only two assists in 21 regular-season games but had a couple of goals in 10 playoff games and contributed regularly. One goal came in Game 1 of the Stanley Cup Final, the only game the Golden Knights won in the series.
Reaves has never scored more than 13 points in a season but has always been a tough guy on the ice. That role has been diminishing as the NHL gets faster, but Reaves showed he had a little more to his game in the postseason.
The Knights also signed defenseman Nick Holden to a $4.4 million, two-year contract.
The Associated Press contributed to this report.