Mrs Foster will replace Peter Robinson, who announced his plans to step down as DUP leader and Northern Ireland first minister last month.
She is the only candidate for leader.
Replacing Mr Robinson became more of a coronation than an election when DUP MPs Nigel Dodds and Sammy Wilson said they would not put their names forward.
Nevertheless, the party's 46 most senior representatives at Stormont, Westminster and the European Parliament will gather at an east Belfast hotel on Thursday, to go through the formality of electing their sole nominee.
Later in the evening, the DUP's 90-member executive will then be asked to ratify her appointment.
Arlene Foster has experience of some of the most high-profile posts in Northern Ireland politics and has long been tipped for Stormont's top job.
The Fermanagh politician  has had a rapid rise through the DUP ranks since joining the party from the Ulster Unionists in 2004.
She was born Arlene Kelly in Roslea in 1970.
Her first experience of Troubles violence came when she was just eight years old.
Her father was a part-time policeman and was shot by the IRA at the family farm.
When she was a teenager in 1988, a bomb exploded under her school bus.
Profile of Arlene Foster
Mrs Foster has represented the Fermanagh and South Tyrone constituency since 2003.
She is Stormont's current finance minister and has twice held the role of acting first minister of Northern Ireland, when Mr Robinson stepped aside temporarily in 2010 and in September this year.
Mrs Foster recently said she has been humbled by the level of support she has received from her party.
Although she is set to lead the DUP from Thursday onwards, she will not take over from Mr Robinson as first minister until 11 January - the day MLAs return to their debating chamber after the winter break.
Senior Democratic Unionist Party (DUP) politicians are set to formally elect Arlene Foster as their first female party leader on Thursday evening.