, who played three Tests for South Africa in 2012.
In total, the Tigers have announced 18 new player contracts since the weekend.
Manu Tuilagi, Telusa Veainu, Noel Reid, Greg Bateman and Kyle Eastmond all left last week, with Jordan Taufua expected to follow.
The 10-times English league champions are second from bottom in the Premiership and seeking to negotiate pay cuts following financial losses as a result of the coronavirus pandemic. Future salary-cap reductions are also a factor.
Players unwilling to agree to the pay cuts were told they could leave the club.
Youngs is England's most-capped scrumhalf, having appeared in 99 Tests for the country. The 30-year-old has made 244 appearances for Leicester since making his debut as a teenager in 2007.
Tigers director of rugby Geordan Murphy said: "It's pleasing to see Ben commit to the club long term. He is, and has been since very early on in his career, one of the world's best in his position."
Flyhalf Ford, 27, who has 69 Test caps, made his debut for Leicester at the age of 16 and has made 90 appearances for the Tigers either side of a four-year spell with Bath.
"He is as professional a player as I have seen in my career, as both a player and coach, and one of the senior leaders at our club," said Murphy.
Taute, 29, joined Leicester in 2019 after three years at Irish club Munster. He previously played for the Stormers and Lions in South Africa.