Mr Duguid had been the UK Government Minister for Scotland, but has now left government, Downing Street confirmed on Friday.
The Banff and Buchan MP was previously a junior minister at the Scotland Office and an assistant government whip.
Mr Duguid will take on the new role of fisheries envoy for Mr Johnson. His replacement is yet to be named at the Scotland Office.
Mr Duguid said it was an “honour” to serve the UK Government for the past 15 months, adding in a statement: “As the MP for a constituency with significant fisheries, agriculture and energy interests, I was particularly glad to provide insight into these key industries.
“I’m very proud of what I’ve been able to help achieve in that post, including the outcomes of the Scottish Seafood Exports Task Force and my influence on the North Sea Transition Deal worth £16 billion to our energy transition to net zero.
“The Prime Minister has asked me to take on a new role as his fisheries envoy which I have accepted and look forward to embracing fully.”
The axing was confirmed as Mr Johnson told his new-look Cabinet they had all made it there on merit, but encouraged them now was the time to redouble their efforts, as he joked about the number of delivery rooms he has been in.
In the first meeting of the new Cabinet on Friday, the Prime Minister said it was time to “spit out the orange peel” and work together, having sacked three people who would otherwise have joined them around the table in Downing Street.
With Cabinet Secretary Simon Case to his right and Chancellor Rishi Sunak to his left, Mr Johnson said: “I want to thank you all because you’re all here on your merits because you’ve worked incredibly hard, but I want you to work even harder now.
“I’m just thinking about delivery. I’ve seen a few delivery rooms, probably seen as many delivery rooms as anybody in this … apart from the exception of Jacob [Rees-Mogg].
“I know that delivery normally involves a superhuman effort by at least one person in the room. But there are plenty of other people in that room who are absolutely indispensable to that successful outcome.”
Dominic Raab, demoted to justice secretary, was sat opposite the Prime Minister, as was Mr Raab’s replacement as foreign secretary, Liz Truss, and new housing secretary Michael Gove.
In other moves announced on Friday, James Cartlidge has been appointed parliamentary under secretary of state at the Ministry of Justice and as an assistant government whip.
Tom Pursglove has been handed the job of parliamentary under secretary of state jointly at the Home Office and the Ministry of Justice, while former nurse Maria Caulfield takes up the same position at the Department of Health and Social Care.
David Rutley has taken up a position as junior minister at the Department for Work and Pensions.
Mr Johnson could meanwhile come under pressure over whether to grant Ms Truss or her demoted predecessor Mr Raab access to the grace-and-favour mansion of Chevening in Kent.
Downing Street suggested no decision had been made.