How do I connect sony wireless headphones to my 2010 iMac?

Although one can state that Bluetooth is backwards compatible, the WF-1000XM3 has BT 5.0 and that mid-2010 iMac supports BT 2.1+EDR. That is a huge gap in the BT standard, and the BT profile implementations. Your only option may be as a wired headphone. If you have the current firmware in the WF-1000XM3 via the Sony Headphone Connect iOS application, and you cannot get them paired, you probably will not.

You can determine what BT profiles are supported by pressing Option-key + menu > System Information… and from the resulting panel, select Bluetooth. Supported services are the BT profiles available in that iMac. Your headphones support A2DP, AVRCP, HFP, HSP profiles, but there is no telling what versions of these profiles are implemented in either device, and what that portends for interoperability with a 2010 iMac.

Thank you for the update.

Anything of interest in the following article?

https://www.sony.co.uk/electronics/support/wireless-headphones-bluetooth-headphones/wf-1000xm3/articles/00199243

See also:

https://helpguide.sony.net/mdr/wf1000xm3/v1/en/index.html

https://everymac.com/systems/by_year/macs-released-in-2010.html

Connect a Bluetooth device with your Mac – Apple Support (UK)

Hi,

Any information about the exact Sony model?

If they're Bluetooth, and in range, once switch on your Mac should see them. Have you open BT and looked?

You are welcome.