The games will be rebranded as the Autumn Nations Series and will include Scotland’s matches against South Africa, Australia, Japan and Tonga.
The UK broadcast deal also covers all of England, Wales, France and Italy’s games, with Ireland’s matches to be included from next year.
Amazon Prime Video took its first steps into rugby coverage last year when it screened the Autumn Nations Cup. It was then credited with an interest in the Six Nations before the Championship agreed a new four-year renewal with BBC and ITV.
The on-demand service is available as part of Amazon's Prime wider subscription or as a standalone offering.
The deal was negotiated with Six Nations Rugby, which is responsible for the distribution of centralised broadcast rights of its six unions and federations’ autumn matches.
Scotland kick off their autumn programme with a game against Tonga on Saturday October 30 (2.30pm kick-off), then face Australia on Sunday November 7 (2.15pm), South Africa on Saturday November 13 (1pm) and Japan on Saturday November 20 (1pm). All matches are at BT Murrayfield.
The kick-off times will be staggered over each weekend so viewers can watch each of the matches involving the home nations.
The Springboks, who will also play Wales and England, head to Europe fresh from their series victory over the British and Irish Lions.
New Zealand are also touring and will take on Wales, Ireland, France and Italy.
Ben Morel, chief executive officer of Six Nations Rugby, said: “We are delighted to be working with Prime Video again for the broadcast of the Autumn Nations Series. They were a fantastic partner last year and we share the same ambition to establish an exciting series that fans will engage with and enjoy.
“We have worked closely with all our unions to agree a schedule of fixtures, that minimises overlaps making it possible for supporters in UK and Ireland to watch every single match from the home teams in a series that will showcase the best teams in the northern hemisphere against the best teams in the southern hemisphere, with Argentina, Australia, New Zealand and South Africa all featuring.
“The series will also be the opportunity for the public to enjoy some of rugby's emerging nations, Japan, Tonga, Georgia and Fiji and witness some of rugby's great growing talents.”
Alex Green, managing director of Prime Video Sport Europe, said: “We are thrilled to continue working with Six Nations Rugby to bring more top-level international rugby union to Prime Video. Our collaboration for the Autumn Nations Cup provided support to the unions member clubs and brought a new tournament to millions of Prime households during a disrupted year in the rugby calendar.
“The Autumn Nations Series will build on that and deliver highly anticipated tests between the best and most exciting teams from the northern and southern hemispheres.”
Prime Video is available to stream from the web or via an app on smartphone, tablet and set-top box including Sky, Virgin, TalkTalk and BT, game consoles, or select smart TVs. Visit Amazon.co.uk/watchanywhere.