◎ 1) He will keep (or fulfill) his promise (or his word).
○ 2) He will make good on his promise (or his word).
○ 3) He will make his promise (or his word) good.
○ 4) He will be true to his word (or his promise).
○ 5) He will be as good as his word (or his promise).
［解説］ どれも英作文で使えるが、1) が最も普通。
◎ 1) keep (or fulfill) one's (or a) promise：約束を守る（なお、「約束する」= make a promise ≒ give one's word、「約束を破る」= break one's (or a) promise (or one's word) ≒ go back on one's word (or one's promise)。
keep one's word : 約束を守る（「約束」を意味する word は不可算名詞で one's word の形で使う）
○ 2) make good on O：O（目的・約束など）を果たす（普通の表現）
○ 3) make O good：（約束などを）履行する、果たす
○ 4) be true to O：O に忠実である、O を忠実に守る
○ 5) be as good as one's word (or one's promise)：約束を忠実に果たす