News of his imminent departure comes a few days after Celtic lost to arch-rivals Rangers on a penalty shootout in the Scottish Cup semi-final.
Celtic's dominance will come under threat next season as Rangers, demoted to the bottom tier following a financial meltdown, returns to the top flight after a four-year absence.
In a statement announcing the news Celtic chairman Ian Bankier said: "The club, as always, will give Ronny our full support until the end of the season.
"We will then make a decision regarding our next manager with the objective of remaining Scotland's pre-eminent club. I thank Ronny and once again wish him well for the future."
In the absence of 54-times Scottish champions Rangers, Celtic have routinely won the title, but have struggled in Europe. This season they were beaten by Malmo in the Champions League qualifying rounds and then failed to survive the group stage of the Europa League.
They were also humbled by tiny Ross County in the semi-finals of the Scottish League Cup.
Deila, who previously coached Norwegian club Stromsgodset, leading them to a first title for 43 years in 2013, said his focus was now on securing Celtic's fifth consecutive title.
"There have been some disappointments and times when we have not achieved what we had hoped for and I'm realistic and honest enough to admit that," he said.
"But I know that starting on Sunday we must all unite and drive the club on and really go for what we all want as Celtic supporters -- to be Scottish Champions once again."
(Reporting by Martyn Herman; Editing by Ken Ferris and Gareth Jones)
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