The Magpies are known to be keen to increase their options up front and they had a £6.9million bid for Gomis rejected earlier this week.
But a fee has now been agreed for the 27-year-old and a deal could be concluded over the weekend if personal terms can be agreed with the France international striker.
Lyon have confirmed the agreement, president Jean-Michel Aulas telling French website Journal du Dimanche: "We have accepted the proposal of Newcastle, which is eight million euros, plus two million bonus.
Agreement linked to agents' fees
"The agreement is now linked to the acceptance of agents' fees. I understand that the problem is in the amount and manner of payment of commissions.
"There are several people involved in the operation, which complicates the negotiations, but I am hopeful that things will be resolved within 24 or 48 hours."
Newcastle only finished 16th in the Premier League last season, after a superb fifth place finish in 2011/12, and they have yet to make any new signings this summer.
They are believed to be interested in signing striker Loic Remy on loan from QPR and now seem to be closing in on Gomis, who is known as 'Baby Drogba' in France and has been capped 10 times.