The Nets also declined to pick up the fourth-year option on guard Maurice Ager.
Boone, Williams and Yi are now signed through the end of next season. Ager will be a free agent at the end of this season.
Boone's option is worth $2.25 million, Yi will get $3.19 million in the final year of his contract and Williams will receive $1.63 million.
Boone was selected with the 23rd pick in the first round of the 2006 NBA Draft. He has appeared in 131 games, averaging 6.3 points and 5.2 rebounds while shooting .557 (337-of-605) from the field.
Williams, drafted 17th overall in 2007, appeared in 73 games as a rookie. He averaged 5.6 points, 4.4 rebounds and his 106 blocks was the second highest block total for a Nets rookie, trailing only Kenyon Martin's 113 in 2000-01.
Yi was the sixth pick in last year's draft. He was traded to New Jersey, along with Bobby Simmons, for Richard Jefferson on June 26. In 66 games with Milwaukee, Yi averaged 8.6 points and 5.2 rebounds.