Edgar, 27, can also play in midfield and has won 23 caps for Canada while Gunning is a former Republic of Ireland under-21 international.
Edgar joins the Blues on a two-year deal from Burnley while Gunning has signed a one-year contract to begin on July 1 after leaving Dundee United.
Born in the Canadian city of Kitchener to an English father, he joined Newcastle as a 14-year-old before turning professional, making his debut for the Magpies in December 2006.
He made 23 appearances for Newcastle before leaving for Burnley in July 2009 on a four-year deal.
While with the Clarets, Edgar made a total of 115 appearances and scored three goals. He also a spent a spell out on loan at Swansea City towards the end of the 2009/10 season.
Last season he made 21 appearances for Burnley as they won promotion to the Premier League.
Gunning, 23, made 99 appearances for Dundee in three years, scoring 10 goals in the process.
The duo are Blues boss Lee Clark's fifth and sixth summer signings, following Jonathan Grounds, Stephen Gleeson, Grant Hall and Wes Thomas to St Andrew's.