I had the same problem (no Wi-Fi on the Pi-3 after migrating a Raspian SD card from a Pi-2)
I tried many of the suggestions above, but what really helped was:
#wget
https://raw.githubusercontent.com/RPi-D ... fw-610.812
#wget
https://raw.githubusercontent.com/RPi-D ... fw-610.812
#wget
https://raw.githubusercontent.com/RPi-D ... 3-sdio.bin
#wget
https://raw.githubusercontent.com/RPi-D ... c43143.bin
#wget
https://raw.githubusercontent.com/RPi-D ... 0-sdio.bin
#wget
https://raw.githubusercontent.com/RPi-D ... 4-sdio.bin
#wget
https://raw.githubusercontent.com/RPi-D ... 9-sdio.bin
#wget
https://raw.githubusercontent.com/RPi-D ... 0-sdio.bin
#wget
https://raw.githubusercontent.com/RPi-D ... 4-sdio.bin
#wget
https://raw.githubusercontent.com/RPi-D ... 5-sdio.bin
#wget
https://raw.githubusercontent.com/RPi-D ... 2-sdio.bin
#wget
https://raw.githubusercontent.com/RPi-D ... 0-sdio.bin
#wget
https://raw.githubusercontent.com/RPi-D ... 0-sdio.txt
#wget
https://raw.githubusercontent.com/RPi-D ... 4-sdio.bin
#mv brcm8* /lib/firmware/brcm/
# rpi-update
*** Raspberry Pi firmware updater by Hexxeh, enhanced by AndrewS and Dom
*** Performing self-update
*** Relaunching after update
*** Raspberry Pi firmware updater by Hexxeh, enhanced by AndrewS and Dom
#############################################################
This update bumps to rpi-4.1.y linux tree
Be aware there could be compatibility issues with some drivers
Discussion here:
viewtopic.php?f=29&t=113753
##############################################################
*** Downloading specific firmware revision (this will take a few minutes)
% Total % Received % Xferd Average Speed Time Time Time Current
Dload Upload Total Spent Left Speed
100 168 0 168 0 0 503 0 --:--:-- --:--:-- --:--:-- 661
100 49.4M 100 49.4M 0 0 780k 0 0:01:04 0:01:04 --:--:-- 707k
*** Updating firmware
*** Updating kernel modules
*** depmod 4.1.21+
*** depmod 4.1.21-v7+
*** Updating VideoCore libraries
*** Using HardFP libraries
*** Updating SDK
*** Running ldconfig
*** Storing current firmware revision
*** Deleting downloaded files
*** Syncing changes to disk
*** If no errors appeared, your firmware was successfully updated to 4bc6b6705e3206f8cd9a316f3343aaf14d62
*** A reboot is needed to activate the new firmware
# reboot