Woods, 21, made his first-team debut appearance at Middlesbrough in the Carabao Cup in October 2018 as a substitute, before being awarded a first starting berth for the cup clash against Colchester United earlier this season.
Midfielder Dreher, 20, earned his first senior appearance in the 5-3 Premier League victory over AFC Bournemouth in May 2019, before sustaining an injury during pre-season.
Speaking after the pair put pen to paper, Chairman Steve Parish said: "We are pleased to reward Sam and Luke with new contracts, and that we are continuing our proud history of developing talented footballers that have risen through our Academy ranks.
"Sam is an extremely committed player that has spent a lot of his time training with the first-team over the last two seasons, and has a firm advocate in Roy.
"Luke is an immensely talented player who has been unfortunate over the last few years with injury. However, we have a real belief in him and if he continues to put everything he has into his rehabilitation, with the full support of our medical and coaching team, we are hopeful he can get back on the training pitch as soon as possible."
Dreher said upon signing: "I’m delighted to extend my contract at Palace. The club have showed great faith in me and I will continue to work extremely hard towards breaking into the first team."
Woods commented: "I’m very happy to have signed a new contract at the club. It’s been a good start to the season for me personally making my full debut against Colchester United, despite the result. Hopefully I can push on now and will continue to work hard and I’m excited to see what the future holds."