The 31-year-old joined Glasgow Warriors last week in a loan deal to run until the end of the season but is understood to have already agreed to become an Exile at the end of the RaboDirect PRO12 campaign.
The prop, who has played 28 times for his country, has been linked with a move south in the past, only to opt to remain at Murrayfield. However, he featured in just eight matches for Edinburgh this season before making the switch to Scotstoun and a subsequent move south at the end of the campaign is now expected to be a formality.
It will bring an end to an eight-year spell at Edinburgh which comprised more than 130 senior appearances for the club. That experience is likely to have attracted London Irish. "We're still going to keep trying to build that pack and the strength in depth," said Brian Smith, the head coach, in an interview with the BBC. "We want more steel in the pack and we have one or two things we want to address in the backs as well."
Edinburgh have been criticised for their part in ushering Cross towards the exit. "The way he has been treated is a disgrace," said Iain Milne, who won the grand slam with Scotland, in an interview with getreading.co.uk.
"Why Edinburgh are thinking of letting Geoff go I can't get my mind around. What makes things absolute madness is that Glasgow will shortly lose Moray Low to Exeter. It would be absolute craziness if both left when something could be done about it by moving Geoff into the vacancy."