The 24-year-old can play both up front and on the wing and has been on loan at Southend United where he scored three goals in cup competition and made eight league appearances.
Morgan has confirmed United have agreed a fee with the Hatters for his signature ahead of discussing personal terms on Monday.
"Leeds have agreed a fee with Luton for me and I should be agreeing personal terms with them on Monday," he told Southend's official website.
"They are a massive club and it's a massive opportunity."