The No. 12 pick by the Montreal Canadiens in the 2007 NHL Draft, McDonagh has 241 points (53 goals, 188 assists) and a plus-142 rating in 530 games for the Rangers and Lightning, and 46 points (10 goals, 36 assists) in 113 NHL playoff games.
"We really like his two-way game, we really like the fact he's big and strong, a strong skater," Yzerman said. "We especially like the character of the person. When he came in, we felt he made us a better team, we knew he made us a better team. When we traded for him, the idea was to sign him and keep him here beyond next year, and we were able to reach agreement on a contract."
McDonagh, who the Rangers acquired in a trade from the Canadiens on June 30, 2009, had NHL career highs in goals (14) and points (43) in 2013-14.
"The team in Tampa [Bay] right now is so deep, so talented and so skilled," McDonagh said. "I can say we have so much depth, we can roll all our lines and keep playing at a good pace and keep everybody fresh as we go through the season. For me personally, I still feel like I can get stronger and get better every summer working on different things that I need to keep improving on. Certainly now that I've been able to get a taste of what Tampa's system is and their style is, [that's] going to help me this summer going into next season."
Miller, 27, signed a five-year, $26.25 million contract with the Lightning on June 26.
Tampa Bay lost the Eastern Conference Final to the Washington Capitals, who went on to win the Stanley Cup.
"When you look at the grand scheme of things, we lost one game, Game 7, where we could have been in the [Stanley Cup Final]," McDonagh said. "If there's anything that I can look forward to is that we will have a similar team to last year. The management told us that we got this far with this group and it's not going to change too much. We will have the majority of the same players back, so we can improve and have a really good summer of training and give ourselves another chance to get over that hump."
NHL.com correspondent Corey Long contributed to this report.