All three are international players.
Price, 29, spent three seasons with Calgary. The six-foot-one, 205-pound receiver missed two months with a hand injury and finished with 34 catches for 544 yards and two TDs.
"Mo is an explosive player who has exceptional speed and outstanding play-making abilities," Ottawa head coach Rick Campbell said in a statement. "He's a CFL veteran who knows the league, knows the game and has a big up-side.
"He has the ability to come in here and make big contributions right away."
Ottawa posted a league-worst 2-16 record in its first season back in the CFL and struggled mightily on offence. The Redblacks finished last overall in scoring (15.4 points per game), touchdowns (24), time of possession (23 minutes 37 seconds) and rushing yards (82.4).
Simmons finished fourth overall in tackles with a team-high 80 and three interceptions in 2014 and was Ottawa's nominee for the CFL's top defensive player and outstanding player awards. The six-foot-one, 223-pound Simmons spent the 2011-'12 seasons with the Toronto Argonauts before joining the Redblacks.