Tucker, who is not ranked in the ESPN 100 for the 2020 draft, averaged 8.9 points and 3.8 rebounds during his junior season in 2019-20.
"This is a difficult decision, but it's the one I want to make to be completely focused on my professional goals over the next few months," Tucker said on Twitter. "My time at Butler has made me a better player and a better person. Thank you to my coaches, my teammates, and everyone at Butler who has invested so much in me.
"I'll miss wearing the Butler jersey and playing in front of Bulldog Nation."
In a statement, Butler coach LaVall Jordan lauded Tucker's maturity and said his decision is supported by the school.