The news outlet and broadcaster reports the fee paid by Saints will be an initial amount of £7m, which could rise to £8m with add-ons. This will be new Saints manager Mark Hughes’ first signing for the club.
It’s been reported elsewhere that Armstrong’s former club, Dundee United, are set to net around £500,000 of Celtic’s transfer sum due to an agreement in place.
The Scotland international is believed to have completed his medical and has agreed a contract with Southampton.
Having only joined Celtic in 2015, Armstrong made 145 appearances for the club, notching 28 goals from out wide in the process. His Glasgow stay saw him help Celtic to consecutive domestic trebles.