The streaming service will have first pick of live games on Tuesday nights, with BT Sport retaining other matches and highlights, The Independent understands.
Reports also suggest the BBC have secured rights to a Wednesday night highlights package, in a midweek Match of the Day show.
An official announcement could be made as early as Friday (30 June).
The broadcast shake-up will coincide with changes to the Champions League format, confirmed by Uefa earlier this year.
From 2024, the competition will expand from 32 to 36 clubs, each playing eight games over 10 match weeks in a single league table format before the knockout rounds.
The number of overall matches will increase from 125 games to 189, meaning more games are on offer for broadcast.
Amazon’s interest in the Champions League has been strong and concrete for some time, following successful launches in the German and Italian marketplaces last season.
By adding the competition to their portfolio, the streaming giant will hold UK rights to both the Premier League and Champions League, as well as other strong pulls in the upcoming rugby Autumn internationals and US Open tennis.
BT Sport have been the sole UK broadcaster for the Champions League since 2015, having paid £1.2 billion for the rights to air the competition between 2022-2024, but are set to share rights in the coming years.