Carlo Ancelotti and Mikel Arteta were both in attendance at Goodison Park as Everton faced Arsenal on Saturday.
Italian coach Ancelotti was confirmed as the Toffees replacement for Marco Silva just over an hour before kickoff.
The 60 year-old, who left Napoli earlier this month, has signed a four-and-a-half year deal to take over on Merseyside.
"This is a great club with a rich history and a very passionate fan base. There is a clear vision from the owner and the board to deliver success and trophies," Ancelotti said in a club statement.
"That is something that appeals to me as a manager and I am thrilled at the prospect of being able to work with everybody at the club to help make that vision a reality.
"I have seen from the performances in the last two weeks that the players are capable of so much."
The three-time Champions League winner was in the directors’ box to watch his new charges, alongside majority owner Farad Moshiri and chairman Bill Kenwright, as Duncan Ferguson took charge of the side for the final time.
"The work Duncan has done is a great credit to him," Ancelotti added, confirming Ferguson would remain as part of his staff.
"Strong organisation, strong discipline and the right motivation are some of the key ingredients in football and I'm pleased that he will be part of my backroom team moving forward."
Also in the directors’ box, sitting aside Arsenal sporting director Edu and a member of his new staff, Steve Round, was new Gunners chief Arteta.
The Spaniard, who captained Arsenal during his playing career, was announced as Arsenal's new head coach on Friday.
Arteta says he will look to change the culture at the club, following his return.
“I don’t want people hiding, I want people to take responsibility for their jobs and I want people who deliver passion and energy in the football club.
“Anyone who doesn’t buy into this, or that has a negative effect or whatever, is not good enough for this environment or this culture.
"There are things to change, absolutely, because they’re not performing at the level that we expect them to.
“I would like to understand why they are not performing, what is lacking and what their needs are.
"And with the way of us behaving and playing, to say Wow, now I understand, I click, I feel comfortable. Let’s go for it. If I get to reach that point, then I can help them.
"Then they will trust me and then they will follow me.”