The moves by the Southeastern Division clubs were announced Wednesday.
Wolski, 25, joins his fifth NHL club. He split time between the AHL and the NHL in 2011-12, scoring four goals and eight assists in 31 games with the New York Rangers and Florida Panthers.
For his career he's scored 95 times to go along with 163 assists in 424 games, with time also spent with Colorado and Phoenix. The Avalanche selected him 21st overall in 2004, but his production was fallen off dramatically since a 2009-10 season in which he recorded career highs with 43 assists and 65 points.
As such, the left wing was signed by the Caps to a one-year contract for $600,000 US. He averaged $3.8 million on the two-year deal that just concluded.
Gragnani is on a one-year, two-way deal.
He scored two goals and 13 assists in 58 games with Buffalo and Vancouver last season.
The 25-year-old was named top AHL defenceman in 2010-11, and at the end of that season was named to Canada's world championship squad.