Rice has been given permission to have a medical at the Emirates after the Gunners met West Ham's valuation.
Talks were still ongoing on Wednesday night over how the payments are structured, but both clubs expect a swift resolution and Rice has been told he is free to discuss personal terms and have medical tests.
The deal will smash Arsenal's transfer record - the £72m they paid Lille for Nicolas Pepe in 2019 - and make Rice the most expensive British footballer in history.
Arsenal have seen off competition from Premier League champions Manchester City to secure the 24-year-old's signature in what will represent a major coup for manager Mikel Arteta.
City ended their interest after having a £90m bid knocked back by West Ham.
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Rice also held talks with Newcastle, but Arsenal were always his preferred destination and they look set to finally get their man after two previous failed bids.
Arsenal's latest offer is worth an initial £100m to West Ham, with performance related add-ons taking the deal to £105m.
West Ham owner David Sullivan told talkSPORT last month that Rice's Europa Conference League final-winning performance would be his last game for the club.
He has played 245 games for West Ham, having come through the club's youth system after being released by Chelsea.
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Arsenal have been working hard in the close season to improve a squad which pushed City hard in the Premier League last season, eventually finishing second.
They completed the signing of Kai Havertz from Chelsea on Wednesday for £65million.
The German forward has made the move across London after three seasons with the Blues, during which he made 139 appearances, scoring 32 goals, including the winner in the 2021 Champions League final.
Meanwhile, Arsenal are also pursuing a move for Ajax full-back Jurrien Timber.