The assistance program agreed on will provide for the allocation of some 86 billion euro ($95 billion) over the course of three years.
Rajoy also noted that the Greek parliament should adopt four laws, as stipulated by the lenders, before the start of the aid plan.
"We must achieve the maximum, and the maximum is that we came to an agreement," Rajoy said, reminding that "the key issue" is the implementation of the obligations by all parties, which will then "lead to economic growth and job creation."
Rajoy stated that the preservation of Greece in the Eurozone is "good news," and added that the "majority wants to be in the Eurozone, and no one wants to leave it."
Rajoy, however, criticized Greece for holding a referendum on a bailout deal, which provoked an atmosphere of "distrust" in the European Union.
An agreement on the third Greek bailout deal was announced on Monday after 17 hours of talks between European leaders who had met in Brussels on Sunday. By Wednesday, Greece is expected to pass the reforms recommended by its creditors, to allow the country to stay in the currency union.