finally; after much effort; in the end
Used after a long process or hard work to express that something finally happened. Often follows a verb in past tense or a noun indicating a period of struggle.
See also: のちに
長い話し合いの末に、ようやく合意に達した。
After long discussions, we finally reached an agreement.
苦労の末に、彼は夢を実現させた。
After much hardship, he finally realized his dream.
at the end of; after (a period)
Used with a time expression to indicate the end of that period. Common with words like 来週, 今月, 今年.
来週の末に、レポートを提出しなければならない。
I have to submit the report at the end of next week.
After lengthy negotiations, the contract was finalized.
At the end of next month, we're moving to a new office.
After agonizing over it many times, he finally decided to study abroad.
結局 simply marks the final outcome of a situation without necessarily implying a long, hard process, whereas 末に stresses the effort or time spent before the result.
後 is a more formal, literary word for 'after/later', while 末に specifically highlights reaching the end of a period or a long process, often with effort.
after a heated discussion; after much debate
From 末 (すえ, 'end') + particle に, literally 'at the end'. The adverbial use developed from the temporal meaning.