The Scottish First Minister will meet the new PM ahead of the British Irish Council meeting - which brings together senior figures from administrations across the UK.
Thursday's talks between the two leaders are expected to focus on the cost-of-living crisis, with Ms Sturgeon likely to stress the importance of avoiding "damaging austerity" measures in the UK Government's upcoming Autumn Statement.
With Ms Sturgeon hoping to hold a second vote on independence in October 2023, she will also use the talks to highlight the "importance of respecting the right of the people of Scotland to choose their own constitutional future", the Scottish Government said.
Mr Sunak spoke to Ms Sturgeon on the phone on October 25 - the day he was formally appointed Prime Minister by the King.
His predecessor Liz Truss did not speak directly to Ms Sturgeon during her brief spell in Downing Street - after saying she would "ignore" the SNP leader.
The Scottish Government confirmed the talks will take place in Blackpool.
A spokesperson said: "Ahead of the 38th British-Irish Council this Friday, the First Minister will hold bilateral talks with the Prime Minister in Blackpool on Thursday afternoon, and take part in a meeting of the Prime Minister and Heads of Devolved Government Council immediately following that.
"The meeting will be an opportunity to discuss the cost-of-living crisis, the need to avoid damaging austerity in the upcoming Autumn Statement, and the importance of respecting the right of the people of Scotland to choose their own constitutional future."