The defender joined the Baggies as a free transfer last summer from Preston North End.
"We always thought as a free transfer Billy was a steal," Downing told the WBA website.
"We have monitored Billy for a number of years, so when contractually it was clear he was a free, it was a no-brainer.
"But, as a person, you just never know whether players stepping up a level or two are going to cut it.
"To have come in and played the number of games he has played, without looking out of place, is testament to the quality of player that he is.