Digital pot (MCP41100) as LED strip dimmer
There are two primary methods of LED strip brightness control (that I know of)... PWM (as mentioned by Jules) and current control. Voltage control is not much use (e.g. using a digital pot as a voltage divider), as the gradient between the LEDs being 'off' and 'on' is so steep, and one also needs to be mindful of how much power is dissipated in the resistor.

A digital pot is redundant if you go the PWM route.

For current control, a digital pot can indeed be used to control the brightness of the strip at the service of a microcontroller. e.g wifi control message > microcontroller > digital pot > dimmer circuit > LED strip.

Current-control LED dimmer circuits are easily found with a quick internet search. They typically use a pot to control a high-gain PNP (NPN + PNP combo). Current-control arguably provides better flicker-free lighting even when dimmed (depending on PWM frequency).

An example current-control dimmer circuit can be found here on GitHub (GlowBall). It uses a manual pot, but that could be substituted with a digital pot (and probably parallel resistor to scale the resistance range appropriately depending on the digital pot resistance). Disclaimer: yes, that's my repo.