Hiller signed a two-year contract; financial terms were not released but media reports place its full value at $9 million.
Hiller, 32, was 29-13-7 with a 2.48 goals-against average and .911 save percentage in 50 regular-season games for the Anaheim Ducks in 2013-14, but he lost his starting job during the Stanley Cup Playoffs to two rookie goaltenders.
He was benched in favor of Frederik Andersen to start the playoffs, and after briefly regaining the No. 1 spot because of an injury to Andersen, the Ducks turned to John Gibson and put Hiller back on the bench during the second round against the Los Angeles Kings. The Ducks lost the series in seven games.
The Swiss goaltender has won at least 26 games in each of the past four full seasons for the Ducks. He has a .916 career save percentage, and a .932 save percentage in 26 playoff games.
"Jonas is familiar with the [Western Conference]," Flames general manager Brad Treliving said. "He's had great success in the League. … Our goaltending got better today."
Treliving said signing Raymond became necessary after forward Mike Cammalleri signed Tuesday with the New Jersey Devils. Raymond's contract is for three years; media reports say it is worth $9.5 million.
Raymond, 29 in September, enjoyed a bounce-back season in 2013-14 with the Toronto Maple Leafs, scoring 19 goals and finishing with 45 points in 82 games. Those were his best offensive totals since the 2009-10 season, when he had career highs of 25 goals and 53 points with the Vancouver Canucks.
The Alberta native was selected by the Canucks in the second round (No. 51) of the 2005 NHL Draft. After spending the first six seasons of his career with Vancouver, Raymond signed a one-year contract with Toronto on Sept. 23, 2013.
"I'm a little lost for words, to be honest," Raymond told the Flames website. "It's a surreal feeling. I think the opportunity to play for the Calgary Flames has always been something I've dreamed of and for this to become reality is something special.
"My wife and my son obviously have a huge impact on my life and my decision and what we decided. Ultimately that was one of the biggest reasons why Calgary was such a good fit. Family is very important to me and something dear in my decision."
Raymond has 99 goals, 223 points and 140 penalty minutes in 456 NHL games.
Engelland signed a three-year contract; financial terms were not released but TSN reports it has an average annual value of $2.9 million.
The 32-year-old had a career-best six goals in 56 games with the Pittsburgh Penguins last season, and had 12 points and 58 penalty minutes. He was held without a point in seven Stanley Cup Playoff games.
In five NHL seasons, all with the Penguins, Engelland has 13 goals, 47 points and 308 penalty minutes in 243 games.
"We wanted to add some bite to our right side," Treliving said.
Engelland said he spoke to Treliving, Flames coach Bob Hartley and president of hockey operations Brian Burke, and all that attention made Calgary the best destination.
"I've talked to Brad and [Burke] and Bob, and they all see more from me in my game if I get an opportunity to play a little more and become more of a leader and a bigger role on the team," Engelland said. "They think I can grow as a player and I do too. They all see more from me in my game if I get an opportunity to play a little more and become more of a leader and a bigger role on the team. They think I can grow as a player and I do too.
"That's a huge part of my decision on where I wanted to go."