Ream was sold to Fulham on August 20, 2015, and signed a four-year contract. The move came with an unknown sum and the opportunity to prolong his stay for another year.

On August 29, 2015, he made his Fulham debut, playing 90 minutes in a 3-1 win over Rotherham United. Due to international commitments and injuries, he only made 29 appearances for the club in his debut season. Following the departure of James Husband, he was utilised at left back towards the end of the season after initially playing as a centre defender. On October 1, 2016, he scored his first goal for the club in a 2-1 loss against Queens Park Rangers.

Ream scored his first Premier League goal for Fulham against Crystal Palace on Boxing Day 2022.