Stanley has played 57 games for the Cats since being traded from St Kilda at the end of the 2014 season.
Abbott was drafted with pick 69 in the 2016 AFL National Draft. The 27-year-old kicked two goals on debut in round 20 against Richmond.
The former Grovedale ruckman retained his place in the Cats side for the remainder of the season and performed admirably in the Cats elimination final defeat to Melbourne.
Geelong general manager of football Simon Lloyd told the club’s website that both players merited new contracts after solid performances in 2018.
“Rhys produced a strong block of games this year where he demonstrated the type of football he can play. He is focused on taking his game to another level through consistency and professionalism,” Lloyd said.
“Ryan had a consistent year, working hard at his craft and was rewarded with an AFL debut late in the season. Ryan shows a lot of drive, we look forward to seeing him develop over the next two years.”
Rookies Jermaine Jones and Sam Simpson have also signed new deals with the club.
Jones earned a one year deal after playing seven games in 2018, while Simpson was awarded a two-year contract, despite playing only one game this season.