accept an offer
take up an offer

Sometimes you may only be given minutes to accept the offer.

He accepted the offer and was involved with the Society for the next 12 months.

They accepted the offer, and in 1636 began major building works.

For several months, he accepted the offer and then moved on to other things.

"Why not accept the offer while you look around for another position?"

But those who accepted the offer would have to pay more for some services, like home health care.

I think you would be better off to accept the offer now.

Was I wrong to accept the low offer in the first place?

Still, in my own name I accept your offer of service.

Only the first 30 people who accepted the company's offer would have a job.