The Spanish frontman has committed to a four-year deal with the Foxes.
Leicester have been in talks for weeks over a deal to sign the Belgium worldwide, who impressed on loan at the King Power Stadium over the second half of the season, and it is understood that it is now progressing towards a positive outcome.
Perez's representatives have already been at King Power Stadium to thrash out personal terms, and a fee of £30m will see the Foxes pick up their second signing of the summer following James Justin's arrival from Luton.
Speaking to LCFC TV, he said: 'I'm very happy and very pleased.
"The club want to keep growing as much as they can and that's something I like".
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But it is Brendan Rodgers' Leicester who have jumped to the head of the queue, and a surprise move will now be completed in the coming days.
"Ayoze will be a wonderful addition to the squad".
The report suggests Mike Ashley is determined to employ someone with Premier League experience, which has made Martinez a top target.
Newcastle won the race to secure his signature back in 2014 when the likes of Barcelona and Real Madrid were trying to lure him away from Tenerife.
Perez, 25, would finish his time at Newcastle with 195 appearances.