The former Arsenal and West Ham winger made the surprising switch on Wednesday night following a conversation with Spireites assistant Mark Crossley, who was a team-mate of Boa Morte's at Fulham.
The 35-year-old last played in England with the Hammers in 2011 and concedes it may take time before he can declare himself match-fit.
"I'm just going to take it day-by-day," he told the club's official website. "It's difficult to say how far I am from full fitness but I am looking forward to just keep doing what I was doing, training, and making myself available to play.
"I've just met the lads, I got a good welcome and I'm just looking forward to get back training and to start playing as well."
On the prospect of him being involved in Saturday's clash with Dagenham, Boa Morte added: "I hope so. I've got a session today (Thursday) and I've got a session tomorrow so the manager will be the one to decide but I will definitely give it my best shot."