Randle has developed into one of the NBA's most versatile offensive frontcourt players.
Randle, 24, had the best NBA campaign of his five-year career last season, averaging 21.4 points on 52% shooting to go along with 8.7 rebounds and 3.1 assists per game for the New Orleans Pelicans.
The Knicks followed the Randle agreement by striking a two-year, $20 million deal with 10-year veteran free agent Taj Gibson, said his agent, Mark Bartelstein. Gibson, 34, is coming off his second season with the Minnesota Timberwolves, in which he averaged 10.8 points and 6.5 rebounds.
The Knicks also landed free-agent forward Bobby Portis for two years and $31 million, Bartelstein told ESPN. Portis, 24, was traded from Chicago to Washington in February and averaged 14.2 points and 8.1 rebounds for the season.
On Monday, the team turned its attention to the backcourt, agreeing to a two-year, $16 million deal with free-agent guard Wayne Ellington, Bartelstein told ESPN.
Randle had signed a two-year, $18 million deal with the Pelicans a year ago in a tight financial market that included a player option -- which he declined to become a free agent. Before his time with New Orleans, Randle spent four seasons with the Los Angeles Lakers, who selected him seventh overall in the 2014 NBA draft out of Kentucky.
NBA free-agent contracts can't be officially signed until Saturday.