Scotland midfield pair McTominay and Gilmour have arrived from Manchester United and Brighton respectively.
Politano said, "They are exceptional: they are different, but they complete a great midfield.
"Two players with personality, who will bring enthusiasm and experience."
On the instant impact of Romelu Lukaku, he also stated: "Lukaku is a fantastic guy, it's always better to have him in a team. I'm happy to have him back, he brings enthusiasm and personality.
"His career speaks for itself. How do you change with Lukaku? Romelu is a point of reference, he protects the ball and makes the team move up: in the open field he's an animal."