Gayle, 25, moved to St James Park for a reported fee of about £10m, swapping the Premier League for the Championship in the process.
Former Real Madrid and Liverpool boss Benitez opted to stay at Newcastle despite relegation last season.
"He is a great manager and has great experience," Gayle told BBC Newcastle.
"There's expectation, but under the manager here I believe he can help me to perform.
"There's a great history at Newcastle - I'm looking forward to getting this club back in the Premier League and proving a few people wrong."
During three seasons at Palace, he scored 26 goals in 74 games following a £6m move from Peterborough.
The journey from Arsenal's academy to non-league football with Stansted right through to scoring goals in the Premier League at Palace echoes the progression of England forward Jamie Vardy.
Newcastle appealed as the next step in his career, with the influence of Palace boss Alan Pardew - a former Newcastle manager himself - strengthening his decision.
Palace's fan 'ultras' have created a pumped-up atmosphere with chanting and banners within the capacity constraints of Selhurst Park, but the size of the attendances and scale of the stadium are incomparable to that of St James Park.
"There was other interest but the opportunity of playing at Newcastle in front of 50,000 is a great one," Gayle added.
"It's great for a player to have the support behind them, it gives you that extra strength. It was the best thing for me in my career."
Rafael Benitez's aura as a manager helped to convince striker Dwight Gayle to drop a division and join Newcastle United from Crystal Palace.