Trollope was confirmed as Russell Slade's successor on Wednesday, although Cardiff chairman Mehmet Dalman declined to disclose the length of the contract at a hastily-arranged press conference.
The 43-year-old joined Wales manager Chris Coleman's back-room staff in July 2015 and says the decision whether he remains in the international set-up will be taken after the European Championship in France this summer.
"I'm due to meet up with the Wales squad in preparation for the Euros and that doesn't change," said Trollope, who will retain the title of head coach he was given when joining Cardiff in February 2015.
"I've got full belief that I've got time to prepare fully for pre-season and the new season ahead.
"Maybe 20 years ago it would have been a problem, but with modern technology in the world today I don't see it as any sort of hindrance to the new season.
"After that I think there will be a discussion moving forward with the FAW (Football Association of Wales), Chris Coleman and the club whether it's viable or not (to continue)."
Trollope has coached at Birmingham and Norwich, but his only previous experience as being the number one came in a five-year spell at Bristol Rovers between 2005 and 2010.
Cardiff's Malaysian owner Vincent Tan has often been accused of interference in team affairs, but Trollope promised he would do the job his way after stepping up from being Slade's assistant.
"It's been well-documented that it's a restructure," said Trollope, the former Wales midfielder.
"But every coach and manager has got their own philosophies, and I'll bring my own style to the job.
"I've got clear ideas of what I want on and off the pitch, not only the way the team plays, but the way professional footballers should act and the discipline they show.
"I've practised that throughout my career, from international level right through to League Two.
"I've already done that in my coaching and managerial career."
Slade was removed as manager at the end of a season in which Cardiff finished eighth in the Championship
The former Leyton Orient and Brighton boss has taken up a new role as head of football at the club.
Trollope, however, will not report to Slade and has identified promotion as very much the target next season.
"We want progress and that means play-offs, and hopefully promotion," said Trollope.
"We have to be ambitious, we have to create a positivity and a real belief within the club.
"If we can take that step - and it is a big step because of the teams coming down from the Premier League and those missing out on the play-offs - then that's what we will be looking to do."
Source : PA
Source: PA