What is a Nonnegative Whole Number?
A Nonnegative whole number is an "integer that is either 0 or positive."
Source: http://mathworld.wolfram.com/NonnegativeInteger.html
In other words, you are looking to validate a nonnegative integer.
The answers above are insufficient because they do not include integers such as -0 and -0000, which, technically, after parsing, become nonnegative integers. The other answers also do not validate integers with + in front.
You can use the following regex for validation:
/^(\+?\d+|-?0+)$/
Try it Online!
Explanation:
^                   # Beginning of String
    (               # Capturing Group
            \+?     # Optional '+' Sign
            \d+     # One or More Digits (0 - 9)
        |           # OR
            -?      # Optional '-' Sign
            0+      # One or More 0 Digits
    )               # End Capturing Group
$                   # End of String
The following test cases return true: -0, -0000, 0, 00000, +0, +0000, 1, 12345, +1, +1234.
The following test cases return false: -12.3, 123.4, -1234, -1.
Note: This regex does not work for integer strings written in scientific notation.