It is the Prime Ministers Mr Johnson's first visit since January and his first since a pro-independence majority was returned in May’s Holyrood election
The Scottish First Minister had invited Mr Johnson to meet at her official Edinburgh residence, Bute House, to discuss the UK’s recovery from the coronavirus pandemic.
But the Prime Minister declined the opportunity, but insisted he would meet with Ms Sturgeon “soon”.
In a letter, Mr Johnson said: “As I noted when we last met, I am keen to arrange an in-person meeting with you and the other first ministers and deputy first minister to build on the constructive discussions we had earlier this summer.
“We agreed then that we should establish a structured forum for ongoing engagement between the Government and the devolved administrations to deliver tangible outcomes in the interest of people throughout the UK.”
Mr Johnson said he was “particularly keen that we work closely together on the vaccination booster campaign this autumn”.
He added: “I look forward to meeting with you soon and working together in the interests of people in all parts of our country.”
The Prime Minister’s itinerary for the visit is not yet known, but he is believed to be in the Central Belt today.
His visit comes at the same time as the Labour leader Sir Keir Starmer, who is focusing on the fight against climate change in the run-up to the United Nations Cop26 climate summit which will see world leaders gather in Glasgow in November.
Sir Keir wrote in the Guardian that the Prime Minister was “missing in action” on the climate agenda.
“The world is looking to Britain, as host of the summit, to deliver,” Sir Keir said. “We cannot afford to miss this moment, but I fear we will.”
The Prime Minister’s visit to Scotland is likely to see further questions about his resistance to a second referendum on independence.
Cabinet Office Minister Michael Gove used a Sunday Mail interview to say the UK Government would not stand in the way of a plebiscite if it was the “settled will” of the Scottish people.