Saudi club Al Qadsiah announced Nacho's arrival on a two-year deal as a free agent on Thursday after leaving Champions League winners Madrid at the end of his contract.
The 34-year-old won six Champions League titles among 26 trophies with Madrid and captained them in their European triumph at Wembley against Borussia Dortmund earlier in June.
On the eve of the 2018 World Cup the Spanish football federation sacked coach Julen Lopetegui after Real Madrid announced he would take over following the tournament.
"This is not my goodbye from Real Madrid, it's to clear up what's happened and explain my decision," Nacho told a news conference Thursday at Spain's Euros base camp in south-west Germany.
"I would have liked (my move) to be sorted out before, thankfully we won the three games and the team is focussed.
"These things don't affect me in the games, I knew it for months and it's made me enjoy things more... all we want is to focus on Georgia."
Spain beat Croatia, Italy and Albania to progress to the Euros last 16 as the only team with a 100 percent record.
They face debutants Georgia in the next round on Sunday and Nacho said he is ready to play after suffering a knock against Croatia in their 3-0 opening victory.
Coach Luis de la Fuente replaced him with Aymeric Laporte as Spain beat Italy 1-0 and Nacho also did not appear against Albania as La Roja again won by a single goal.
"It's been a long season and against Croatia I didn't end up feeling good, and we stopped for a few days to recover," said Nacho.
"Tomorrow I will do the whole training session with the team and I will arrive at the game ready, and after that the coach will decide who plays."
