Maguire completed an £80 million ($98m) move to United at the start of August, bringing to an end one of the year's longest-running transfer sagas.
The 26-year-old was handed his full United debut in an opening weekend clash against Chelsea, which Ole Gunnar Solskjaer's side won 4-0.
Maguire was rock solid at the back, earning the man of the match award while helping the Red Devils earn their first Premier League clean sheet since February.
United followed up that result with a 1-1 draw at Wolves and a disappointing 2-1 home defeat to Crystal Palace on Saturday, which has raised familiar questions over the team's top-four credentials.
However, Maguire's performances have been a real plus for United, with backup goalkeeper Grant already convinced that the English centre-back feels at home in Manchester.
“It’s been seamless,” Grant told United's official website. “Harry has definitely slotted straight in, in terms of the social side and in terms of his mentality and attitude, which has been first class.
“The most important thing, though, is his quality and he was able to show that against Chelsea. We could all see he is quite at home in front of the Old Trafford crowd and quite at home as a Manchester United player.”
Dalot echoed Grant's comments, insisting Maguire is "ready" to be a key player for United over the course of the season.
“He’s so calm," the Portuguese full-back said. "He’s settled in perfectly. He’s a very nice guy, very humble, very quick to settle.
"We’ll keep helping him, but I think he’s already shown everyone on the pitch that he’s ready for this club.”
Solskjaer's side dropped to fifth in the Premier League after their shock defeat to Palace, with a trip to Southampton up next on Saturday.
The Norwegian boss insists that a lack of clinical edge has cost United in their last two outings, with Paul Pogba and Marcus Rashford both guilty of missing from the penalty spot.
The Red Devils will be desperate to get back to winning ways against the Saints, with an international break set to follow the latest round of fixtures.