Speaking with BBC Sport, Vasseur has now opened up on the signing of the seven-time world champion, suggesting that he had been in long-term contact with the Brit before he decided to make the switch.
This is despite Carlos Sainz being told publicly in the winter break by Ferrari chairman John Elkann that he was just as much part of Ferrari's long-term plans as Leclerc.
Vasseur discussed Hamilton transfer
Frenchman Vasseur said that it was important to make the announcement early to ensure that there were no distractions for the team heading into 2024.
He added that the arrival of Hamilton, who he worked with in GP2 when the latter won the title in 2006, will be a 'good challenge' and that the move 'came naturally'.
"We had a good relationship for a bit more than 20 years," said Vasseur.
"We were always in contact and it came like this, step by step."
The Brit’s soon-to-be team-mate Leclerc said that he was made aware of Ferrari’s talks with Hamilton before he committed his future to the team in a multi-year deal, but stressed that it makes little difference to him.
"These kind of deals are not finalised overnight," said the Monegasque driver.
"It takes time and I was aware of those discussion before signing my deal so it didn't come out as a surprise after signing.
"For the rest I don't want to comment that much, mostly out of respect for Carlos.
"We have had great years and we will do everything we can do to finish on the most successful note possible.
"Lewis is an incredible driver, the most successful in history, with a lot [of] experience he will bring to the team and to me," he continued.
"It was good that the team was transparent [about Hamilton], but it didn't change anything for me."