The Lakers did not announce financial terms, but a source told ESPNLosAngeles.com's Ramona Shelburne that the deal is worth $48.5 million.
Bryant, 35, will maintain his status as the NBA's highest-paid player over the course of the extension, the source told Shelburne. The 2007-08 league MVP will receive $23.5 million in the first year and $25 million in the second year of the extension, according to the source.
The Lakers and Bryant arrived at the salaries so that the team will have the financial flexibility to pursue one top free agent on the market next summer, the source told Shelburne.
Bryant and 39-year-old point guard Steve Nash are the only players signed to significant contracts for next season with the Lakers, who have been anticipating a major roster restructuring in 2014 since Dwight Howard fled town in July.
Even if the Lakers waived the oft-injured Nash under a special provision limiting his salary cap hit, Bryant would eat up roughly a third of the team's room under the projected cap before anybody else joins him next season.
Bryant, who has not played since suffering a torn Achilles tendon in April, will make more than $30.4 million this season, the final year of his current contract.
The source also said the Buss family was unified in wanting to see Bryant continue to be the league's highest-paid player, and that the owners wanted the extension finalized before Bryant's return to the court as a way of demonstrating his importance to the franchise.
The team announced the deal in a news release, saying the signing "should ensure" that Bryant finishes his storied career with the Lakers.
"This is a very happy day for Lakers fans and for the Lakers organization," general manager Mitch Kupchak said in the release. "We've said all along that our priority and hope was to have Kobe finish his career as a Laker, and this should ensure that that happens.
"To play 20 years in the NBA, and to do so with the same team, is unprecedented, and quite an accomplishment. Most importantly, however, it assures us that one of the best players in the world will remain a Laker, bringing us excellent play and excitement for years to come."
Bryant, who has helped the Lakers win five NBA championships, took to Twitter on Monday morning, posting a photo of his signature on the contract.
The Lakers also posted a photo of Bryant signing the deal on their Twitter account.
Bryant is the Lakers' all-time leading scorer and ranks fourth on the NBA's career list. He returned to practice this month but isn't sure when he'll be back in uniform.