The former Villa centre-back officially ended his playing career earlier this week after a lengthy career that included spells with Villarreal, Olympiacos and Juventus.
The 36-year-old won a mammoth 117 caps for the Swedish national side, and PSG striker Ibrahimovic played alongside his former teammate for 11 years.
Mellberg, who was one year into a two-season contract with FC Copenhagen confirmed his intentions on Thursday.
He said: "Today I ended my contract with FC Copenhagen, which will be the last in my football career."
Following the announcing, Ibrahimovic issued an open letter to the veteran defender, and thanked him for their time spent together with the European nation.
Often praised and derided in equal measure for being cocksure and aloof throughout his playing career, the sublimely-gifted Ibrahimovic showed a different side to his personality with his heartfelt message to his friend.
He said: “The day Olof Mellberg decided to quit the national team it was a great loss to Swedish football and the team. But to me personally it was an even greater loss. When I had him on the team I never had to look back because I knew he was behind me and I could concentrate on what was going on up ahead.
"Olof was the person that triggered and challenged me. This drove me to want to do more on the pitch.
"Olof had a winner mentality like no other. He simply refused to lose, not only in football but in practically everything. And when he did lose, which rarely happened, he refused to admit it. I think this mentality was what took him a long way in his carreer.
"I’ve been doubly lucky when it comes to Olof. Firstly because I got to play with him, and secondly because I got know the person Olof Mellberg, not only the player. If Olof in my opinion is the best Swedish defender of all times, I think the person Olof is even better.
"It is sad that Olof now chooses to end his career because I’m sure he has much more to give. "I wish Olof Mellberg and his family all happiness and love in the future."
A mainstay of the Swedish side, Mellberg was part of the squads that took part in the 2002 and 2006 World Cups in Japan/South Korea and Germany, and he also played in four European Championship campaigns from 2000-2012.
Mellberg made 227 appearances for Villa in a seven-year period from 2001-2008 before departing for Juventus, and he hangs up his boots with two Greek Super Leagues and a Danish league and cup double, which was won in his final season.