The phrase "accepts your resignation" is correct and usable in written English.
You can use it in a formal context when acknowledging someone's decision to resign from a position.
Example: "We regret to inform you that the company accepts your resignation effective immediately."
Alternatives: "acknowledges your resignation" or "consents to your resignation."
In accepting your resignation effective April 20 , 1993 Professor Wrighton agreed that MIT would continue to pay your full salary and benefits through June 30 , 1994
As a result, you offered to resign from National Review, the celebrated conservative magazine founded by your father, William F. Buckley Jr. Did you expect your editors to accept your resignation?
Roosevelt sent Barkley a "Dear Alben" message that, after recounting their differences vis-à-vis the tax bill and assuring Barkley that he didn't doubt his good faith, went on to "hope your colleagues will not accept your resignation; but if they do, I sincerely hope that they will immediately and unanimously re-elect you".
Update from Editor Erick Schonfeld: I accept your resignation.
Paul, thank you for your contributions to TechCrunch, and I accept your resignation.
"It is with enormous regret that I accept your resignation as the MP for Corby and East Northamptonshire, a seat that had been Labour for thirteen years before you," the PM said.
When the company has formally accepted your resignation letter, formally advice your colleagues of your status.
It helps to know the language in the letter to the NSA which would prompt the NSA to accept your resignation easily and soon.
"I am not accepting your resignations," Reese pompously announces upon returning.
In journalist John Barr's telling, as Aberhart and Hugill left the meeting the premier said "your resignation is accepted, Hugill", while according to Elliott and Miller he said only "you know what this means, don't you?" Whatever the words used, Hugill resigned later that afternoon.
