Wilson took on the role in June 2018, and led the side in 25 games as full-time captain. Ireland finished third in the T20 World Cup qualifier under his leadership, taking them to the first round of the tournament itself in Australia next year, and won 12, lost 12 and tied one of his games at the helm.
Andrew White, the chairman of selectors, said that his panel and Wilson had agreed Balbirnie should "have the opportunity to forge his leadership style and his standards across all three formats", and praised the "number of exciting young players" that had been brought through during his tenure.
"Both Gary and the selectors believe that Andrew Balbirnie should have the opportunity to forge his leadership style and his standards across all three formats," White said.
"Whilst he was announced as Test Match and ODI captain a few weeks ago, after consultation with the selectors and Gary it was agreed by all that with similar players likely to be utilised across all formats it was important that Andrew was allowed to stamp his mark on the new generation of players coming through."
"Gary has been an inspirational leader and our qualification was largely down to his attention to detail in planning and getting the best out of his players in a short space of time. We thank Gary for his candour and professionalism during this process. He will remain an integral part of the international setup as we continue to build this exciting group of young players."
Wilson said it was an "absolute honour" to have captained his country.
"It was something that I dreamt about as a child," he said. "When I took on the job 18 months ago it was always the remit to qualify for the [T20] World Cup and reassess from there.
"I'm very much looking forward to continuing as a player and working with Balbo in the future. I think it will prove to be a great appointment and believe that it is important that he, as a captain, has control of all three sides and gets to take it in a direction that he sees fit."
Head coach Graham Ford said: "Gary has been an exceptional leader of this young squad over the last 18 months, and it has been his experience, incredible passion for Irish cricket and clarity of thinking that has been the major contribution to the team's exciting progress over the last 18 months and qualifying for the T20 World Cup.
"It is a mark of Gary's professionalism that he has understood the interests of the team, and wholeheartedly committed his full support to Andrew in his newly consolidated leadership role."