The Jazz announced the move Monday but did not disclose terms. Gobert tweeted a picture of himself signing the paperwork with the caption "4 more years!"
Finalizing the deal in advance of Monday's 11:59 p.m. ET deadline allowed the Jazz to avoid restricted free agency on Gobert in July. The contract will fall just shy of the projected max of $106 million.
"It will be done today," a source close to the talks said earlier Monday.
Gobert had told the Salt Lake Tribune this month that he was prepared to wait until restricted free agency in July, if necessary, but sources said Utah was motivated to get a deal done before the extension window closed for 2013 first-round picks to ensure that its defensive anchor stayed off the open market next summer.
The Jazz are undoubtedly hoping that re-signing Gobert helps them re-sign star swingman Gordon Hayward in July if Hayward, as expected, opts out of the final year of his contract to become an unrestricted free agent. Utah could also try to reach terms on an extension with Derrick Favors, Gobert's frontcourt sidekick, during the season; Favors became eligible for an extension on Oct. 19.
Gobert, 24, was drafted No. 27 in 2013 and has career averages of 7.2 points, 8.6 rebounds and 2.0 blocks per game.