“That Works for Me” Means the Arrangement Suits Me

When arranging a time, someone might ask, “Friday at three?” Replying, “That works for me” means the arrangement suits you; it does not mean that something is doing a job for you. Here, work means to be suitable or practical. The tone is neutral and cooperative, and the phrase can be used for times, places and plans.

“That is convenient for me” is not wrong, but it is more formal; in an everyday discussion, “That works for me” sounds more natural. If you are still uncertain, say, “That should work for me.” The phrase confirms only that you can make the arrangement. It does not decide on behalf of anyone else.

https://dictionary.cambridge.org/dictionary/english/work
https://www.collinsdictionary.com/dictionary/english/work