Typing an object created dynamically through a loop in Typescript

I have a type like this:

type Wrapper<T> = {
    [K in keyof T]: {
        value: T[K];
        meta: string[];
    }
}

I have a function createWrapper that takes an object and creates a wrapper out of it:

const createWrapper = <T extends object>(obj: T): Wrapper<T> => {
    let wrapper: any = {};
    for (let key in obj) {
        wrapper[key] = {
            value: obj[key],
            meta: []
        };
    }
    return wrapper as Wrapper<T>;
}

How could I type the object creation inside createWrapper to avoid any and as Wrapper<T> types?

Thanks a lot for the help!