In Star Trek: The Next Generation established that Picard was promoted to iral in order to lead the Federation's rescue mission to save the Romulan people when their star went supernova in the 2380s. Worf was serving as Picard's First Officer so the chain of command made him the natural choice to be promoted to the big chair, but Starfleet had serious reservations about the Klingon.
Worf was the first Klingon to Starfleet and he had a colorful career where he starred in twoEnterprise-D was destroyed, Worf ed Deep Space Nine as Strategic Operations Officer, where he served under Captain Benjamin Sisko (Avery Brooks). Worf also married Lt. Commander Jadzia Dax (Terry Farrell), who was murdered by Gul Dukat (Marc Alaimo) at the end of DS9 season 6. Worf briefly became Chancellor of the Klingon Empire by killing Gowron (Robert O'Reilly) but he ed the Chancellorship to General Martok (J.G. Hertzler). At the conclusion of the Dominion War, Worf became the Federation Ambassador to the Klingon Empire but he soon returned to Starfleet and the Enterprise-E in Star Trek: Nemesis.
Worf's ascendance to commanding the Enterprise is detailed in the canonical prequel novel, Star Trek: Picard: The Last Best Hope by Una McCormack. When news of the Romulan supernova reached Starfleet, Picard was summoned to Starfleet Headquarters in San Francisco. In a meeting with Commander-in-Chief Victor Bordson and Captain Kirsten Clancy (Ann Magnuson), Picard accepted a long-overdue promotion to iral in order to lead the Romulan rescue mission. But this meant Picard had to immediately relinquish command of his beloved Enterprise so, naturally, he suggested Worf, his current First Officer to become the new Captain. But Clancy balked at Worf getting the big chair and for good reason: the Klingon has a permanent black mark on his record. In the DS9 season 6 episode "Change of Heart", Worf allowed a Starfleet Intelligence operative to during a secret mission, choosing, instead, to rescue his injured wife Dax on the planet Soukara. Afterward, Captain Sisko told Worf that "[Starfleet will] probably never give you a command of your own after this."
Captain Clancy was correct to raise this disciplinary issue with Worf taking command of the Enterprise, which is the flagship of the United Federation of Planets. Picard argued for his First Officer's spotless record since that incident, which occurred almost a decade before this meeting. As to the question of Worf's judgment, Picard noted that the memory of that mistake makes Worf even more careful about his decision-making. Picard was also offended at the idea that he would select Worf to be his First Officer if he didn't think the Klingon was capable of being a worthy Captain someday.
Picard won the argument when he pointed out that a century prior, during the events of Star Trek VI: The Undiscovered Country, the Klingons came to the Federation for help and they eventually became such staunch allies that a Klingon rose to the position of commanding the Federation flagship. Jean-Luc's point was that the Romulans could see the symbolism, which would help them understand what was possible in a long-term peace with the Federation. Clancy finally relented and she itted that "The optics were good". With that, iral Picard officially relinquished command of the Enterprise to the newly-promoted Captain Worf.
Worf commanded the U.S.S. Defiant on DS9 so he has plenty of experience leading a starship. But while the Klingon is certainly deserving, he also can't help but seem like the best of Picard's available options since Will Riker (Jonathan Frakes) left to become Captain of the U.S.S. Titan and Commander Data (Brent Spiner) died in Star Trek: Nemesis. Star Trek: Picard: The Last Best Hope also noted that another reason Picard had to vacate the Enterprise was that the flagship's long history of conflict with the Romulans could have sent the wrong message in a peaceful rescue mission. This helps explain the Enterprise-E and Worf's absence from Star Trek: Picard, since the beloved starship was in deep space continuing its mission of exploration while Jean-Luc Picard saved the galaxy once again.