Hamburgers have totally become a part of Japanese food culture.
Hamburgers have completely become rooted into Japanese food culture.
Hamburgers have completely become a part of Japanese food culture.
すっかり--> completely/totally
日本の食文化--> Japanese food culture
根付く--> become a part of/take root in
纏めったら
「直訳」
"Hamburgers have completely become rooted into Japanese food culture"
「もう少し単純な言い方で」：
"Hamburgers have totally become a part of Japanese food culture"
アメリカ合衆国 
