The Muse singer tied the knot with the 29-year-old model in front of family and friends and took to social media to share the news of their big day.
Captioning photos from the wedding, Matthew and Elle wrote in separate posts, "Mr. & Mrs. Bellamy," alongside a string of adorable emojis.
Matt and Elle got engaged during a trip to Fiji in December 2017.
Alongside a picture of the pair riding horses on the beach, Elle wrote at the time: "Was going to surprise everyone on Christmas, but just can’t wait any longer ... We are so happy to announce to the world that we are engaged! Just a few days after my birthday, on the most romantic holiday of our lives, the man of my dreams asked me to marry him! After tears of joy, gasps of shock, and a split second of disbelief, of course - I said YES! I can’t imagine our lives apart. What I can imagine is a bright future full of love & light, family & friends, moments that turn into cherished memories, and a lifetime of pure bliss (sic)"
Matt had previously revealed he is "pretty happy" with Elle and is thankful to have contentment in his own life when things in the wider world are so chaotic.
He said: "In my personal life, I'm pretty grateful, pretty happy. But when you look at what governments and corporations have done to the planet with warfare and environmental destruction, there's a constant feeling of discord."
And asked his tour essential, he added: "A girlfriend. That makes touring easier."