Both games are deemed to be first team fixtures, and the same group of players are likely to contest both games.
The Welling game will kick-off at 3.00pm, followed by Greenwich Borough at 7.30pm.
The Addicks will start their pre-season campaign in Ireland this year. They will fly to the Emerald Isle in early July, before contesting three games.
The games will be staged on Monday 10, Tuesday 11 and Wednesday 12 July. Karl Robinson’s men will then fly home to play the Welling and Greenwich Borough games at the weekend, to complete a sequence of five games in a week.
It was announced last week that Ipswich would travel to The Valley on Saturday 29 July to provide the opposition in Charlton’s final warm-up game.
The Addicks will also play games on Saturday 22 July, and in midweek during weeks commencing 17 and 24 July.
It will be a brutal first week of warm-up fixtures, following an intense training regime.
Robinson’s team should not be lacking in fitness when the season proper starts.