Mellanby ended his 21-year career after Atlanta made the playoffs for the first time in its seven-year history, but lost four straight games to the New York Rangers.
"I've been fortunate to live my dream for the past 21 years, and it's with a heavy heart that I'm retiring from the National Hockey League," the 40-year-old right-winger said. "I'd like to thank all of my great teammates, the fans who have supported me, and all the wonderful people I have met along the way."
Mellanby played in 69 games, with 12 goals and 24 assists this season.
He entered the league with the Philadelphia Flyers in 1986 and played for Edmonton, Florida and St. Louis before spending his last two seasons with the Thrashers.
In 1,431 regular-season games - tied for 17th on the NHL's career list - Mellanby had 364 goals, 476 assists and 2,479 penalty minutes. He also appeared in 136 playoff games, scoring 24 goals and adding 29 assists.
He reached the Stanley Cup final with Philadelphia in 1987 and Florida in 1996 but never won the ultimate prize.