The deal is set to cost Nationwide around Â£500 million, according to a spokesperson for the building society, and will create a group with assets totaling some Â£150 billion.
This should allow the companies to make significant cost reductions in what is becoming an increasingly competitive and difficult home-loan market, and allow building societies to continue competing successfully against the much larger retail banks.
The new company will have 13 million members, second only to HBOS in the UK market.
It is expected that the merger will see most Portman branches rebranded as Nationwide, although a spokesperson said that the details and potential overlaps of the two businesses would be looked at in due course.
Although agreed by the boards, the deal between the two building societies is still subject to the approval of Portman members, due to meet early next year.