Although the £27 million ($34m) transfer has yet to be announced, the Gunners have seen off competition from north London rivals Spurs to sign the highly-rated centre-back.
Saliba is currently away with Saint-Etienne in the United States and will return to Europe after the French side’s game against Marseille on Sunday.
He is then due to travel to England for his medical before completing his move to the Emirates. He will sign a five-year deal and will spend the coming season back on loan with Saint-Etienne.
Arsenal are delighted to have got their man, with the Gunners having scouted Saliba extensively since the turn of the year following his breakthrough into senior football in Ligue 1.
There were fears they could lose him at the last minute after Spurs launched a late move for the defender, but Saliba’s preference was always to join Arsenal.
Once confirmed, he will be the north London club’s second signing of the summer following the arrival of Brazilian teenager Gabriel Martinelli.
And Arsenal are hopeful that further new additions will follow, potentially by the end of next week - with the capture of Ceballos set to be finalised in the coming days.
Talks have progressed well with the Spanish giants and they could even be concluded in person when the two teams meet in Washington on Wednesday night in the International Champions Cup.
Like Arsenal, Madrid are already in the United States and will take on Bayern Munich on Sunday in Houston.
Ceballos has not travelled with the squad, however, as he is still on holiday due to his involvement with Spain Under-21s at the European Championship earlier in the summer.
He is due back next week and Arsenal are hopeful a deal can be wrapped up swiftly for the attacking midfielder, who will spend the season on loan at the Emirates.
Arsenal will pay Madrid a loan fee for the 22-year-old, while also covering his wages - believed to be around £3m a year.
A third bid is also being prepared for Kieran Tierney, with Arsenal looking to finally come up with a package that Celtic find acceptable for the left-back.
The Scottish champions are holding out for £25m ($31m) for Tierney and want the majority of that fee paid up front.
Arsenal’s second offer did total £25m, but Celtic were unhappy with the structure of the deal - which included around £7m ($9m) worth of bonuses.
Unai Emery is also hoping to land another centre-back before the end of the transfer window, with a new winger also a priority.
Wilfried Zaha remains Emery’s No.1 target, but a move for the Crystal Palace star continues to look unlikely due to the £80m ($100m) price tag Palace are demanding.
Arsenal saw a £40m ($50m) offer rejected for Zaha earlier in the summer and are expected to make another approach, with Emery open to including some of his fringe players to sweeten the deal.
Zaha - an Arsenal fan - is desperate for a move to the Emirates, but he has not submitted a transfer request.
But sources at the Emirates insist there is nothing in the speculation coming from South America and that the 23-year-old is not on their list of potential targets.