The issue of who appoints bishops has been at the heart of a dispute since China first broke off diplomatic ties with the Holy See in 1951.
China has some 10 million Catholics.
Pope Francis hopes the deal "will allow the wounds of the past to be overcome" and bring about full Catholic unity in China, the Vatican said.
An eighth bishop, who died last year, was also posthumously recognised by the Vatican.
Beijing has long insisted that the state must approve the appointment of bishops in China, running contrary to the Catholic Church's insistence that it is a papal decision.
Currently, Catholics in China face the choice of attending state-sanctioned churches approved by Beijing or worshiping in underground congregations that have sworn allegiance to the Vatican.The "provisional agreement" was signed in Beijing by China's deputy minister for foreign affairs, Wang Chao, and the Vatican undersecretary for state relations, Monsignor Antoine Camilleri.
It is thought in future bishops will be proposed by the Chinese authorities and then approved by the Pope, the BBC's James Reynolds reports from Rome.
Beijing said it hoped the accord would lead to better relations with the Church.
The Vatican described it as "the fruit of a gradual and reciprocal rapprochement", which had followed a "long process of careful negotiation" and would allow for periodic reviews.
The move potentially opens the way towards the establishment of diplomatic relations between the Vatican and China, our correspondent says.
But critics - including the Archbishop of Hong Kong - say the Vatican's decision to reach an agreement with the Communist Party is a betrayal.
No mention was made of Taiwan in Saturday's announcement. The Vatican is the only European diplomatic ally of Taiwan, which is viewed by China as a breakaway province.
Taipei said it had been assured by Rome that the deal was "not of a political or diplomatic nature" and would not affect their 76-year-old diplomatic relationship.
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