NFL Network's Michael Lombardi reports the extension is worth $60 million over six years.
Ferguson had one year, plus an option year, remaining on his rookie deal signed in 2006, worth a total of $13 million.
The Jets are expected to announce the deal Thursday.
The star tackle, who switched agents to sign with Brad Blank in February, will get $34.8 million in guaranteed money, and his average of $10 million per season matches Dolphins OT Jake Long's record for an offensive lineman, a team source tells NFL Network's Jason La Canfora.
The total of Ferguson's contract is now worth $73.622 million, with $60 million in new money.
Unlike his teammates, Ferguson worked very quietly and without public display to get his new deal, a factor in him becoming the first of their young core players to get his extension, a source with knowledge of the situation told La Canfora.
Revis said he wants to become the highest-paid player at his position and the Jets are reportedly willing to offer him a contract worth over $100 million.
Ducasse is expected to start at guard for the departed Alan Faneca, but could also back up Ferguson at OT, where he played at college.
The Associated Press contributed to this report.