The Dromore man will fill the vacancy created by the transfer of Agriculture Minister Edwin Poots to South Belfast following the death of Christopher Stalford.
On Monday morning, the Electoral Office for Northern Ireland confirmed the move.
Mr Rankin, a councillor on Armagh City, Banbridge and Craigavon Borough Council, will be in the role for just two weeks ahead of the dissolution of the Assembly at the end of March for fresh elections.
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The DUP has not yet confirmed which candidates it will run in the Lagan Valley constituency.
The constituency has been the subject of speculation as to whether DUP leader Sir Jeffrey Donaldson, who represents Lagan Valley in Westminster, will run for an Assembly seat.
When he was first elected DUP leader last year, Sir Jeffrey indicated his intention to return to the Assembly.
On Friday evening, Sir Jeffrey said that in Lagan Valley his party is reviewing whether it will run three candidates, as it intended, to maximise unionist representation.
Former First Minister Paul Givan and Mr Rankin are now the DUP’s two MLAs for Lagan Valley.
Sir Jeffrey said: “I am delighted to welcome Paul Rankin to the DUP’s Assembly Team, to serve the people of Lagan Valley. Paul has a sterling record of hard work and delivery for the people of this area, with over 20 years of experience as an elected representative.
“I have worked closely with Paul for many years to champion the case for Lagan Valley and its people. I know he will be a diligent and dedicated servant of their interests in the Northern Ireland Assembly.
“In just over 50 days, the people of Northern Ireland will have the opportunity to set the future direction of our Province. The DUP has a plan to build a better Northern Ireland and to ensure progress is achieved on the basis of moving forward together.
“I look forward to taking this positive vision to the people, leading from the front, so we can deliver our plan for a better Northern Ireland.”