The 21-year-old, who has represented England Saxons, made his Exeter debut back in 2012.
"We've known for a long time that he's a good player and we keep telling everyone that he's a good player," Chiefs director of rugby Rob Baxter told BBC Sport. "I'm delighted we've got all our young players signed up.
"He's going to be staying at the club long term. There's not been an issue with him staying, but there's been some paperwork to sort."
Slade kicked two penalties on Friday night as Exeter earned a 25-22 victory away to Gloucester Rugby in the league.