The 25-year-old signed for the Royals from Nottingham Forest at the start of the summer and made his home debut in a friendly against Crystal Palace on Saturday.
And McCleary is now excited to get the season started on Saturday as his new club host Stoke City in their first game on their return to the Premier League after a four-year absence.
McCleary told the club’s official website: “It’s exciting – I can’t wait to get started.
“It will be a tough game against Stoke but if we go out and do what we can do then we’ll hopefully get three points.
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“We know how they play and they’re a good team. They’ve been established in the Premier League for a while now and they do their job really well.
“But we’ll try and get the ball on the wings and use our strength in depth to our advantage.”
McCleary also expressed delight with his new side’s performances during pre-season and hopes they can continued that form.
McCleary added: “We played really well against Palace - especially in the second half. We created a lot of chances and managed to get the ball in the box a lot. It was great for our strikers to score too.
“All the wingers we’ve got here are really direct, and like to get close to the byline and cross the ball. For me it’s brilliant that I’ve been able to play.”