Atletico said Reyes would have a medical on Tuesday morning and then be presented to the media before joining the squad on a pre-season tour to Amsterdam.
Spanish media have reported that the deal was worth between nine and 12 million euros (£8.1 million).
If the reports are accurate, the move takes Atletico's close season spending up to 70 million euros (£47.35 million) following their purchases of striker Diego Forlan, winger Simao Sabrosa, and midfielders Cleber Santana, Luis Garcia and Raul Garcia.
Drenthe keen to make Madrid move
Reyes almost joined Atletico last year but turned them down in favour of a loan move to city rivals Real Madrid, and as a result was forced to pay Atletico compensation.
The 23-year-old, who has won 21 Spanish caps, made 30 appearances with the nine-times European champions, mostly as a substitute, and scored six league goals.
He came on a substitute and scored twice in the 3-1 win over Real Mallorca on the final day of the season. The win secured Real the Primera Liga title.
Reyes joined Arsenal from Sevilla for a then club-record fee of around £17 million in January 2004 but struggled to adapt to his adopted country.
He had made it clear he did not want to return to Arsenal after his loan period with Real ended.