Elway took to social media to announce the news, one day after the Broncos finished with a 5-11 mark in Joseph's first season as an NFL head coach.
"Vance and I had a great talk this morning about our plan to attack this offseason and get better as a team," Elway wrote on Twitter. "We believe in Vance as our head coach. Together, we'll put in the work to improve in all areas and win in 2018.
"To all our fans: THANK YOU for your tremendous support and sticking with us through a tough year. This wasn't the season anyone expected, but we'll learn from it and be better because of it. Our 2018 season starts today."
One report by ESPN, prior to the Broncos' season-ending 27-24 loss to Kansas City, indicated it was unlikely that Joseph would be back. The 45-year-old admitted he was aware of the report on Sunday, but remained optimistic and said that the team is headed in the right direction.
"I want to be here," Joseph said. "It's a football team that's close. We have to make some adjustments in some places, but our football team has not stopped working. That was fun to see, even (Sunday). It's been a hard year, but everyone kept fighting. I want to be here to fix it."
Joseph replaced Gary Kubiak after the latter stepped away from coaching because of health concerns.
The Broncos' eight-game losing streak from Oct. 15-Dec. 3 was their longest since 1967; six of those losses were by double digits and four by at least 20 points.