The 27-year-old was banished to the reserves side in the first half of last season and then spent time on loan with Hull City, having failed to win over boss Ronald Koeman.
Niasse appears to have reignited his Goodison Park career all of a sudden, however, after following up his first goal for the club in the midweek EFL Cup win over Sunderland with a vital league double against Bournemouth on Saturday afternoon.
"It is a great moment for me at Everton," he told reporters. "I have been waiting for that moment for a long time. I always believed I would have moments like that here. I have kept fighting. Every time there was a difficult time for me, I always tried to do my best.
"I didn't sign for another team – I signed for Everton. So even if I didn't have the chance at the beginning, now the coach has given it to me and I have to take it with both hands. I am thankful for that, but I know I have to keep going, keep working hard.
"We showed really good character as a team [against Bournemouth]. Down 1-0 at home, having lost three [Premier League] games in a row, it was very difficult. But the confidence is back and we want to keep it for as long as we can. We have quality in the team.
"We have had a bad start in the league but after the win in the week, we have got another one so I am happy for the team now. Hopefully this game can start a good run for us."
Niasse will play no part in Everton's Europa League meeting against Apollon Limassol on Thursday night, though, as he was not registered in their 26-man squad for the group stage of the competition.