The 29-year-old completed a surprise switch to Goodison Park on Monday for a reported fee of £20million (€22.4m) after falling out of favour at Real Madrid.
He has won an array of team and individual honours, including two Champions Leagues, and was one of the stars of the 2014 World Cup as Colombia reached the quarter-finals.
That is in stark contrast to Everton's recent exploits, the Merseyside club having gone 25 years since beating Manchester United in the FA Cup final for their last major trophy.
However, with midfield pair Abdoulaye Doucoure and Allan also being brought in for a reported £42m, James insists Everton can achieve something special under Carlo Ancelotti.
"I've come here to this top club to achieve big things," he said ahead of Sunday's trip to Tottenham. "I think the club means business.
"A club that's serious about wanting good things to happen. It's got a lot of history and is a big name. I'm here to do well and I think we're able to do that together.
"There's a lot of serious-minded people in the club at all levels who are determined to achieve, and that will mean winning trophies.
"It won't happen overnight – it's a long-term project. But I've seen signs we can make progress. Trophies are definitely more than a possibility."
Ancelotti played a key part in James' decision to join Everton, with the pair having worked together at Madrid and Bayern Munich.
"He has influenced me a lot. It's great to be back having a chance to work with the manager once again," James said.
"We enjoyed a great season together in 2014 and got on well as a manager and player. It's been such a good choice to reunite with the manager."
Everton endured another underwhelming campaign last time out, finishing down in 12th place despite a mini revival when Ancelotti replaced Marco Silva in December.
But the veteran Italian coach, who like James boasts a number of major honours, believes he now has a strong enough squad to compete for a place in the top six.
"The goal we want to achieve is to fight for the first positions in the Premier League, to be able to reach Europe for the next season," he said.
"The goal is quite clear, we have this desire, this ambition, and I think we can achieve it.
"Our fans want a club and a team that is competitive in the Premier League and so I think that we can satisfy this desire this season and we're going to do our best for this.
"The players that arrived understood that we have a project with ambition for the future.
"This is also the reason they decided and are happy to come here and be here now. They are going to work to give their best for the club."
Asked if supporters can expect any more arrivals before the window closes next month, Ancelotti said: "With these three signings we did a fantastic job.
"The market will be closed on October 5. There are going to be some opportunities and we can look for this. But honestly, I'm satisfied with the squad in this moment."