Redden, who had a down year with the disappointing Ottawa Senators last season, weighed several offers throughout the day before agreeing to terms with the Rangers on a six-year deal that will pay him $6.5 million per season.
"In our opinion he's the best first-passer in the game," Rangers general manager Glen Sather said. "He moves the puck up exceptionally. He's somebody that we had targeted immediately. He was our No. 1 guy on defense, as well as Rozsival.
"We wanted to get them both signed, and we did. We're quite happy that we've got them. We think that's going to help us move the puck to the forwards as well as anybody in the league."
Rozsival returned to New York, where he spent the previous three seasons, for a four-year deal worth $20 million. He was one of the Rangers' key unrestricted free agents, along with Jagr, Avery, and Brendan Shanahan.
Sather didn't stop on the blue line Tuesday, also working out deals with forwards Aaron Voros, Patrick Rissmiller, and Andreas Jamtin from Sweden, and re-signing backup goalie Steve Valiquette.
None of what the Rangers did Tuesday will preclude them from chasing other players, Sather said, most notably Jagr, Avery and Sundin.
"We'll still be active tomorrow. We have other people we're still interested in," Sather said. "No, it doesn't take us out of the hunt for anyone yet."
Sather spoke to Jagr's agent during the day Tuesday and got the impression that situation would be resolved soon - perhaps as early as Wednesday. While the sides are negotiating, it is not following a typical path of offers being passed back and forth.
Still, Sather is confident Jagr would be interested in a deal the Rangers have put out there. Sather believes Jagr might be waiting for leading free agent forward Marian Hossa to sign somewhere before making his decision.
"I don't know whether he has anything else that he's interested in at this time, but we'll just have to wait and see," Sather said. "He knows that we would like to have him back, I've said that 100 times. Where it's going to stand tomorrow or the next day, I can't tell you. That's something he is going to have to decide for himself."
Avery is a different issue. The prime agitator is believed to be seeking a four-year deal in the neighborhood of $4 million per season. That price tag could be out of the Rangers' range.
Sather doesn't know for sure what the terms will be since Avery's representatives didn't return a message left by the Rangers GM - something that had Sather a bit miffed.
"I was a little surprised especially when I called and left him a message. Maybe he was busy doing something else." Sather said.
"I would assume what they're trying to do is shop Sean around.
"We would still like to have him back, but I told him at the onset of this process that things will happen fast so make your mind up. We'll just have to leave it and see where things are (Wednesday)."
Sundin, the captain of the Toronto Maple Leafs, is in Sweden and is believed to be weighing offers from four teams - along with deciding whether he wants to return to the NHL. The Vancouver Canucks reportedly offered a two-year, $20 million deal, which would make Sundin the highest paid NHL player.
"I'm optimistic that we've made the best offer he can receive," Canucks GM Mike Gillis said Tuesday night. "We think we present an opportunity he would like."
Redden was looking for the same after scoring only six goals and 38 points in 80 games with the Senators, who were knocked out in the first round last season after reaching the 2007 Stanley Cup finals.
"The time has definitely come for me to move on. A fresh start is going to be exactly what I need to rejuvenate myself," he said.
"I feel I've got a lot to offer the Rangers on the ice and off the ice. I'm certainly looking forward to a new beginning and a new chapter."
Voros, who had seven goals and seven assists along with 141 penalty minutes last season with the Minnesota Wild, agreed to a three- year, $3 million deal.
Rissmiller posted eight goals and nine assists in 79 games with the San Jose Sharks.
