A last minute agreement has been reached between Turkey, Finland and Sweden to allow the two Nordic countries to become Nato members on the eve of the military alliance's summit in Madrid.

Nato said a trilateral deal had been reached at a meeting between Turkey's president, Recep Tayyip Erdoğan, President Sauli Niinistö of Finland and the Swedish prime minister, Magdalena Andersson, in the Spanish capital.

After a period of intensive negotiations, Jens Stoltenberg, Nato's secretary general, said on Tuesday evening: “I am pleased to announce that we now have an agreement that paves the way for Finland and Sweden to join Nato.”

“Turkey, Finland and Sweden have signed a memorandum that addresses Turkey’s concerns, including around arms exports and the fight against terrorism,” he added.

Andersson hailed the deal as a “very good agreement”, rejecting claims that she had conceded too much to Erdoğan in order to persuade him to drop his veto.

“Taking the next step toward a full Nato membership is of course important for Sweden and Finland. But it’s also a very important step for Nato, because our countries will be security providers within Nato,” she told Agence France-Presse.

Andersson said she had shown the Turkish leader changes in Sweden’s terrorism legislation set to come into force next month.