Areas that will benefit from this investment include Aberdeenshire, Angus, Moray, the Highlands and Perth and Kinross.
Gigabit broadband is 40 times faster than standard super-fast broadband, and allows users to download an HD movie in less than 30 seconds.
The investment is part of Prime Minister Boris Johnson's target of achieving at least 85% gigabit-capable UK coverage by 2025, which officials have said is "on track" to be met.
At present, the UK has 57% coverage, up from less than 6% in 2019, according to the Department for Culture, Media and Sport.
567,000 properties in remote parts of Cheshire, Devon, Dorset, Somerset, Essex, Herefordshire, Gloucestershire, Lincolnshire, East Yorkshire and North Yorkshire will also receive a gigabit speed boost, as part of a £5 billion gigabit rollout project.
Digital Secretary Nadine Dorries said: "The latest stage of our £5 billion Project Gigabit plan will help hard-to-reach homes and businesses out of the broadband slow lane and plug them into the fastest and most reliable connections available".
"This investment is levelling up in action - building new internet connections in our rural communities so people have the speed, reliability and freedom to live and work flexibly, and take advantage of new technologies."