The 28-year-old will ply his trade in the Premier League next term after six seasons at Shakhtar, who have won the last four Ukrainian Premier League titles.
But now his focus will switch to regaining the league crown with City, who surrendered their title to neighbours Manchester United last season.
"I'm relieved," he told Globo. "It was a big battle. The negotiations were intense, took several days and I even abandoned my vacation.
"Everybody left after the league was over but I stayed in Ukraine to convince the club to release me as the buy-out fee was really very high and nobody would pay that.
"When the first offer came in, they said no. I insisted a lot in order to convince the manager, the board and even the captain.
"I had meetings with the president who promised he would talk with Man City if an offer of 40 million euros came, which finally happened.
"The truth is that I wanted to leave Shakhtar after eight years there. I told them this. As I was loved there, respected by the fans and within the club, they gave up.
"But I think they demanded such a high fee just to find out how much Man City wanted to sign me. Also, knowing Ukrainian culture, they were afraid someone would offer a lower fee and sign me."
Fernandinho has only picked up five caps for Brazil in his career despite regularly impressing in Ukraine, and he believes playing regularly in the English top flight will boost his chances of featuring at the 2014 World Cup on home soil.
"The national team was certainly something that I took into account when I made my decision," he added.
"I had a stable life in Ukraine. I had adapted and I was loved by the club. But I was left out of the national team in early 2012 and didn't get called up again. That really affected me.
"Then this chance to move to England came. I wanted to go as it will give me more visibility, both in Brazil and Europe. Now my chances of returning to the national team will certainly be a lot bigger."