The 40-year-old Spaniard will take over subject to him obtaining a visa, which the club applied for last week.
Selles took charge of Southampton following Nathan Jones' departure in February but only won two of his 17 matches at the helm as Saints finished bottom of the Premier League.
He succeeds Paul Ince, who was sacked by Reading in April.
Selles takes over a Reading side that were relegated to League One last season after having six points docked for breaching the terms of a business plan for a previous profit and sustainability rule infringement.
The club are currently under a transfer embargo from the English Football League resulting from that breach, the non-payment of loan wages and not reporting financial details of His Majesty's Revenue and Customs.