"We are establishing embassies to replace the liaison offices that we had," Tsipras announced during a joint press conference with Zaev, as broadcast by the ERT television channel.
The prime minister is currently paying his first visit to North Macedonia, where he has held a meeting with his counterpart, Zoran Zaev, in Skopje.
The move became possible after North Macedonia, formerly known as simply Macedonia, changed its name under the 2018 Prespa agreement with Greece.
Athens had been opposing its neighbor's use of the name "Macedonia" for years because it was also the name of a region in Greece, but the deal and its subsequent ratification put an end to the years-long dispute.