"The playoffs felt great," Alfredsson told local reporters in Sweden, indicating that he also suffered no back problems.
"I needed a few weeks to see if the necessary urge for summer training and pre-camp was there. And it is."
In 47 games with the Sens last season, Alfredsson has registered 10 goals and 16 assists for 26 points. He won the Mark Messier Leadership Award on Friday.
It's believed Alfredsson will receive a salary between $4.5 million and $6 million.
Alfredsson, 40, has played in 1,178 career regular-season NHL games, all with the Senators, and has accumulated 426 goals and 682 assists for 1,108 points, and 500 penalty minutes.
He was originally drafted by the Senators in the sixth-round (133rd overall) of the 1994 NHL Entry Draft.