Mbappe has informed Paris Saint-Germain that he will be leaving the French outfit when his current deal expires at the end of the 2023-24 campaign.
The France international is widely expected to make the move to Real Madrid on a free transfer, and Henry has said that his arrival at Bernabeu could mark the start of a period of domination for Los Blancos.
"If you look at it properly, if Mbappe goes to Real Madrid they will have a team that can dominate Europe and La Liga for maybe six or seven years because they will all be young, Mbappe, Vinicius [Junior], Rodrygo, [Federico] Valverde, [Aurelien] Tchouameni," he told CBS Sports.
Mbappe has again been in impressive form for PSG this season, scoring 34 goals and registering seven assists in 34 appearances in all competitions.
Real Madrid will not have to pay a transfer fee for the 25-year-old, but it is still expected to be one of the biggest deals of all time when his wages and signing-on fee are taken into account.
Carlo Ancelotti's side are on course for success in La Liga this season, currently sitting top of the table, seven points clear of second-placed Girona.
Meanwhile, Real Madrid booked their spot in the quarter-finals of the Champions League courtesy of a 1-1 draw with RB Leipzig in the second leg of their last-16 tie earlier this week.
Henry also praised the capital outfit for their ability to move players on at the right time, with the squad continually being refreshed.
"What they do very well is to know when to get rid of players. I don't mean players that it's logical to get rid of. I mean it was time for Cristiano Ronaldo," Henry added.
"It was time for Casemiro. It was time for Mesut Ozil. It was time for [Raphael] Varane, who I think was out with a knee problem.
"There's one thing you have to give Real Madrid a lot of credit for, and that's the ability they have to make sure they build a team by keeping the old guard to make sure they can pass on to the guys coming in, to the youngsters they sign."
Real Madrid will be bidding to return to winning ways when they welcome Celta Vigo to Bernabeu in La Liga on Sunday evening.
Ancelotti's side have only won one of their last four matches in all competitions, which proved to be a 1-0 home success over Sevilla in La Liga at the end of February.