Pip, 17 bytes

aR-C+XL.C+XD{c.b}

Takes input as a command-line argument. Try it online!

This uses the standard regex-replacement strategy. Explanation of golfing tricks will appear shortly.

Pip, 17 bytes

aR-C+XL.C+XD{c.b}

Takes input as a command-line argument. Try it online!

Explanation

This uses the standard regex-replacement strategy, somewhat golfed.

The regex is -C+XL.C+XD, which evaluates to `(?i)([a-z]+)(\d+)`:

   XL       Preset regex variable for lowercase letter: `[a-z]`
  +         Apply + to the regex: `[a-z]+`
 C          Wrap the regex in a capturing group: `([a-z]+)`
-           Apply the case-insensitive flag: `(?i)([a-z]+)`
        XD  Preset regex variable for digit: `\d`
       +    Apply + to the regex: `\d+`
      C     Wrap the regex in a capturing group: `(\d+)`
     .      Concatenate the two regexes: `(?i)([a-z]+)(\d+)`

The replacement is {c.b}, a callback function that concatenates the second group (c) and the first group (b). (The first argument to the function, a, contains the whole match.)

This is three bytes shorter than the naive aR`(\D+)(\d+)``\2\1`.