Smithies, who began his professional career with Huddersfield Town, joined QPR in August 2015 and made over 100 appearances for the second-tier Championship club.
"He's a lad that knows he will have to fight for his place," manager Neil Warnock told Cardiff's website https://www.cardiffcityfc.co.uk. "Neil Etheridge had a fabulous season in 2017/18 and improved as time went on. It's great for us to have that healthy competition."
Smithies, 28, made 43 league appearances for QPR last campaign.
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Reid, 25, has featured 158 times across all competitions for Championship side Bristol since his senior debut in 2011 and was the club's top scorer last season, netting 21 goals in 52 appearances.
"I want to show my high energy and work rate, as well as being creative and working for the team. I’m buzzing to get started," Reid said.
The pair's arrival at Cardiff follows that of winger Josh Murphy and defender Greg Cunningham earlier this month as the Welsh club prepare for their first top-flight season since the 2013/14 campaign.
(Reporting By Arnab Paul and Aditi Prakash in Bengaluru; Editing by Amlan Chakraborty and David Stamp)
