There's no any built in way to do this. However I'd run just a oneliner to achieve what you need.
However you need to know your process id of the bg process (in your case
wget). You could run
ps aux | grep wget
Once you have the PID, You can use
wait . However this doesn't work if you closed the previous shell or session.
In that case I'd use
ps -p PID with a
while loop to fire sleeps while the process is active and after process stopped
while statement ends and shell will execute your
Full code goes as:
while ps -p YOUR-PID > /dev/null; do sleep 1; done && echo "Subject: WGET DONE!" | sendmail email@example.com
summery of above code: while your selected PID process runs
while condition becomes true and loop keeps executing
sleep 1 and it checks for it's condition every one second. However if the process ends
while condition becomes false and the while loop will end. And the shell will execute the command after && which is