Yes it means he accepts. To agree with means to agree about an idea, opinion of another person. "I agree with you." means I think your idea is correct. "I agree to" means you are prepared to do something for the other person. "He agreed to let me go early" - he accepted my request to leave early.

agree with someone agree to something

Presumably you are asking which preposition to use, rather than how to use an infinitive after "agree". The answer is this. We agree with a person. We agree to a plan, a scheme or a proposal.

The grammar for your sentence "My boss…" is to do with "agree + to-infinitive", and not "agree to". Some verbs are used with a "to-infinitive". Examples: I hope to see you tomorrow. We can afford to go on a holiday. She claims to be the Queen. My boss agreed to give me a pay rise. (He said yes.)