Everton manager Martinez confirmed on Tuesday that a deal had been struck to bring the Ghana international to Goodison Park.
And the Spaniard expects Etsu to seal his switch to Merseyside two days before his side's Premier League opener at newly promoted Leicester City on Saturday.
"We're very close to announcing a new signing, I think it's been an open secret in the last few days." Martinez told Sky Sports News.
"We're expecting Christian Atsu to join us tomorrow, the deal is done with Chelsea.
"After the season that we had, it was important that we faced Europe and all the demands this season with the strong backbone that we have, and new blood to bring something a little bit different."
Atsu spent last season on loan at Vitesse and is still awaiting his first-team debut for Chelsea.
The 22-year-old played all three games for his country in the World Cup in Brazil as they finished bottom of Group G.
