Cattaneo, currently executive vice president of high-speed train operator Italo, succeeds Francesco Starace, who has led Enel since 2014 but not found favour with the inner circle of Prime Minister Giorgia Meloni, who took office six months ago.
Enel is one of the world's biggest renewable energy players, with almost 60 gigawatt of installed capacity.
However, under Starace's watch the company has seen a significant increase in debt.
With Meloni determined to put her stamp on major state-controlled firms, the ministry also proposed Roberto Cingolani as CEO of defence group Leonardo, ousting former banker Alessandro Profumo.
Matteo Del Fante was confirmed as head of postal service Poste Italiane.
Government officials said the new CEO of power grid Terna is likely to be Giuseppina Di Foggia, currently head of Finnish telecoms group Nokia's operations in Italy. The announcement is expected on Thursday.
In a 2025 industrial plan presented in November, Enel pledged asset sales worth 21 billion euros ($23.08 billion) to cut its debt pile, and since then it has announced sales deals in Argentina, Romania and Peru.
Several shareholders had signalled to Rome that they did not want an abrupt change in Enel's strategy, in particular a drastic reduction in the group's international footprint. Some investors fear that Enel may come under government pressure to focus on its domestic market.
Environmentalists have questioned Meloni's commitment to the ecological transition after her government rowed back on some of Italy's previous Green pledges.
The Treasury also chose a new chairman for Enel, tapping Paolo Scaroni who is a former CEO of both Enel and Eni.
Cattaneo's appointment was something of a surprise as Stefano Donnarumma, current head of Terna, had been widely touted in recent days as the most likely successor to Starace.
DESCALZI RECORD AT ENI
Unlike Starace, Descalzi quickly won Meloni's backing. With another three-year mandate as CEO, he is on course to become the longest-serving company head at Eni since its foundation in 1953.
The veteran executive, who has held the job since 2014, last year helped Rome secure alternative gas supplies as Moscow curtailed its flows to Italy following Russia's invasion of Ukraine.
Descalzi is now expected to help the Meloni government in its flagship plan to turn Italy into a major energy hub, distributing gas from North Africa and the Mediterranean to the rest of Europe, the government officials said.
Despite having won plaudits from investors for Eni's financial results, Descalzi's strategy is still the target of criticism by energy transition advocates, who say the company should spend more on its green businesses.
The Treasury indicated Italian tax police general Giuseppe Zafarana as Eni chairman.
At Leonardo, the new chief Cingolani has a background as a physicist, and was energy minister in the previous government led by Mario Draghi.
He informally advises Meloni on energy policy, and was previously Leonardo's chief technology and innovation officer.
Former NATO Senior Civilian Representative to Afghanistan Stefano Pontecorvo will be the new Leonardo chairman.
($1 = 0.9098 euros)
(Editing by Gavin Jones)
By Giuseppe Fonte, Angelo Amante and Francesca Landini
