Warning: SPOILERS for Star Trek: Discovery season 3, episode 3, "People of Earth".
Star Trek: Discovery has a new Captain and the series made the best possible choice: It's Saru (Doug Jones). The question of who would ultimately become the new, permanent commander of the U.S.S. Discovery was left hanging at the end of Star Trek: Discovery season 2. Saru and Michael Burnham (Sonequa Martin-Green), who both held the rank of Commander, agreed to table the issue until after they completed their time-travel to the 32nd century.
The U.S.S. Discovery's captain's chair has had several occupants since Star Trek: Discovery season 1. The Crossfield-class starship was originally a science research vessel before it was pulled into the Klingon War of 2256-2257 (that Michael Burnham instigated), and its original Captain was Gabriel Lorca (Jason Isaacs). But Lorca was actually from the Mirror Universe and he used the Discovery to return to the alternate reality. But when Discovery jumped back to its proper Prime Universe, First Officer Saru stepped up as Acting Captain. In Star Trek: Discovery season 2, Captain Christopher Pike (Anson Mount) left the U.S.S. Enterprise and took command of the Discovery. In addition, the Mirror Universe's Emperor Philippa Georgiou (Michelle Yeoh), who also crossed over into the Prime Universe, posed as her counterpart, Captain Georgiou, and sat in Discovery's captain's chair. Plus Admiral Katrina Cornwell (Jayne Brook) also briefly served as Discovery's Captain.
The Discovery was long overdue for a permanent Captain and it was always going to come down to Burnham or Saru, with the expectation that they would discuss who should ultimately accept the starship's command. Shockingly, at the start of Star Trek: Discovery season 3, episode 3, "People of Earth", Michael voluntarily relinquished her bid and insisted that Saru should be Captain. Commander Burnham noted, correctly, that Saru had served with honor as Acting Captain and that he deserved to be recognized as what he already was in the eyes of the crew (and Trekkers): the true Captain of the Discovery. Saru is, indeed, the best choice to be Captain and this was the correct decision for the starship and for the series as a whole.
Not only is Saru absolutely qualified but, as Michael noted, he had been doing the job all along. Saru repeatedly stepped up as Acting Captain during Discovery's constant game of musical chairs during seasons 1 and 2; indeed, the Kelpien embodies the finest ideals of Starfleet and he has earned the respect, admiration, and loyalty of his crew. Saru has been a mentor to Ensign Sylvia Tilly (Mary Wiseman) and he is a seasoned, battle-tested commander. Yet, despite already being firmly in command, the fact that Saru was still willing to discuss Burnham taking the Captain's chair also speaks to his sense of fairness and the quality of his character.
While Michael is also qualified, she admirably has the self-awareness to recognize her limitations, which would be a hindrance if she became Captain of the Discovery. Although Burnham redeemed herself, regained her rank, and she is now 930 years away from her gravest mistakes, it wasn't too long ago in her own (and others') memories that Michael's profound error of judgment started the Klingon War, got Captain Georgiou killed, and Burnham was imprisoned as Starfleet's first mutineer.
Michael has also changed in the year she was alone in the 32nd century before the Discovery arrived in the future, in profound ways she is still grappling with. Burnham realizes that her experiences in that year largely divorced her from the sense of duty to Starfleet that dominated her adult life. It's not even clear how much Michael wants to be aboard the Discovery at this point, although she agreed to be Saru's First Officer. Ultimately, Burnham was right to relinquish her bid for command and insist that Saru officially become the Captain he deserved to be. Recognizing that Saru should be Captain instead of her also speaks to Michael's character and how much she loves Saru, which is wholly reciprocated.
Best of all, Captain Saru represents another breakthrough for Star Trek because the Kelpien now has the distinction of being the first truly alien starship captain of a Star Trek series, following in the groundbreaking footsteps of the first black Captain, Benjamin Sisko (Avery Brooks) of Star Trek: Deep Space Nine, and the first female Captain, Katheryn Janeway (Kate Mulgrew) of Star Trek: Voyager. Although Michael Burnham remains Star Trek: Discovery's lead character, it's fitting that Saru now gets to take his rightful place in the pantheon of Star Trek Captains and add the legend he is still writing to theirs.