The MLA, who currently represents Lagan Valley, said the family of the late Christopher Stalford asked him to do so.
DUP Agriculture Minister Edwin Poots is to replace Christopher Stalford as the party’s MLA in South Belfast.
Mr Poots said he is making the move from Lagan Valley at the request of Mr Stalford’s family.
Mr Stalford, a 39-year-old father of four, died suddenly last month.
Sir Jeffrey Donaldson made the announcement at Mr Stalford’s constituency office in South Belfast on Monday.
“We are bound by the rules of the Assembly which requires us to appoint a replacement within seven days of a vacancy arising,” he told media.
“Edwin (Poots) has been selected to be the member for south Belfast, to continue following in Christopher’s footsteps in representing the people of this constituency.”
Mr Poots will also stand in the South Belfast constituency in the imminent Assembly elections.
There had been some apparent uncertainty over which constituency Mr Poots would stand for the Assembly elections in.
The DUP currently has two of the five Assembly seats in Lagan Valley, with Mr Poots and former first minister Paul Givan.
Sir Jeffrey had indicated he planned to stand in the Assembly elections when he became party leader to return to Stormont.
He is currently the MP for Lagan Valley.
Sir Jeffrey said the party has almost concluded its selection process for the Assembly elections.
“We just now need to select candidates in Lagan Valley and then we will be in a position to ratify all of our candidates,” he said.
Mr Poots described feeling regret at “standing here of necessity” following the death of Mr Stalford.
“I stand here with a lot of regret, we have lost a good colleague and friend in Christopher Stalford,” he said.
“We are standing here of necessity, more than anything else.
“Last week the (Stalford) family spoke to me and asked me would I consider taking on the role of MLA for south Belfast and it was on that basis that the party asked me to take on this responsibility.
“I have a hard act to follow.
“It is also with regret that I leave the constituency of Lagan Valley.
“Sometimes you have to make hard decisions and that is the decision I have made and I believe it is a decision that will bring some degree of comfort to the family that they have someone with the same values as Christopher representing this constituency.”