Al-Thani will purchase the majority stakeholding owned by president Fernando Sanz, a former player who has run the La Liga club for four years and will continue to be linked to them in an advisory role.
"The agreement has already been notified to the (government-run) Spanish Sports Council and will be completed shortly, given that said public body has provided its verbal approval of the agreement's terms and conditions," the club said.
Al-Thani was quoted as saying: "Our goal is to help Malaga take the necessary steps to consolidate its presence in La Liga and to reinforce the excitement and hopes of the supporters."
The sheikh, 43, manages a business empire based in the United Arab Emirates which employs around 3,000 people and operates in more than 30 countries.
His interests include hotel chains, shopping centres, mobile phone companies and car dealerships. Al-Thani is also vice-chairman and shareholder of the Doha Bank.
A business associate of the sheikh, Abdullah Ghubn, told a news conference on Friday that the negotiation process had lasted four or five months.
"In principle the agreement is to take over the shares owned by Fernando Sanz for a price of 36 million euros that includes the club's debt," Ghubn said.
"We are aware this is the first time an investor from this region has come to Spain and he wants to set a good example. We want to consolidate the club in La Liga and afterwards to aspire to higher things."
Ghubn said coach Juan Ramon Lopez Muniz would not continue in his post and that a replacement would be announced shortly.
Malaga are a modest club whose highest league finish was seventh. They have been a 'yo-yo' side over the last 30 years and returned to the top flight again in 2008.
They avoided relegation on the last day of the season in May, to finish 17th in the standings.
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