Melvin will co-host the program with Savannah Guthrie during the 7 and 8 a.m. blocks.
"I am beyond excited and grateful... I want to obviously thank NBC and the folks here who deemed me worthy," he said.
Melvin said he's happy his parents are still alive to witness him in his new role, and thanked his wife and children for their support.
Melvin currently co-hosts the third hour of Today.
"Craig, you are made for this job," Kotb said. "You were literally made for this job. You are that kinda good. You have all the things that this job needs. You're the right person for it."
Kotb's last day will be Jan. 10. She announced in September she was leaving the program after 17 years to spend more time with her children.
Longtime NBC meteorologist Al Roker congratulated Melvin via Zoom, saying, "I knew this day would come. I watched you grow, I've seen you as a journalist. But more importantly, I've seen you as a dad, as a son - all the things that make you who you are. I am so proud and so happy for you right now because you are so worthy of this."