The financial details were not released on either deal.
"Travis Moen is a character player. He is versatile, and he plays hard. His size and style will contribute to adding physicality to our team," said general manager Bob Gainey in a statement.
Moen spent 2008-09 with the San Jose Sharks, scoring seven goals with nine assists over his 82 games. Over his five NHL seasons Moen has scored 29 goals and 27 assists. He won a Stanley Cup with the Anaheim Ducks in 2007.
The native of Swift Current, Saskatchewan was originally drafted by the Calgary Flames in the fifth round (155th overall) of the 2000 NHL Entry Draft.
Mara helps the Canadiens fill a need on the blue-line.
"Paul Mara will bring size and experience to our group of defensemen. He can contribute to all facets of the game," said Gainey.
In 76 games last season, the Ridgewood, New Jersey native had five goals and 16 assists along with 94 minutes in penalties for the New York Rangers. In 10-seasons, the 29-year old has 63 goals and 176 assists while splitting time between the Lightning, Coyotes, Bruins and Rangers.
Mara was originally selected in the first round by the Tampa Bay Lightning, 7th overall at the 1997 NHL Entry Draft.