The 32-year-old started his career in the youth system at Everton before moving to Blackburn Rovers to complete a scholarship and turn professional with the Ewood Park club and making a number of appearances in the Premier League for the club.
In January 2007, Derby County signed the defender for a reported fee of £600,000 and he helped the club to promotion into the Premier League via the play-offs in his first season.
Impressive performances for Derby helped him into the senior Scotland international set-up and he made his debut in August 2007 against South Africa.
After three and a half years at Pride Park, he moved to join Championship outfit Barnsley with whom he made close to fifty appearances before being loaned to Swindon Town.
That loan spell culminated in the Robins winning the League Two title and McEveley joining the club on a permanent basis.
He spent two years at the County Ground before moving to Sheffield United where he made close to ninety appearances and was club captain.
Last season, McEveley made twenty-eight appearances for Scottish Premiership side Ross County, helping the Staggies to a seventh-place finish in the league.
Rovers manager Micky Mellon is delighted to add the left-sided defender to his squad and said: "Jay is someone who we have tracked for a number of weeks and I'm really pleased to add him to the group.
"He's a left footed player which will help give us balance and prevent us from being exposed down that side.
"Jay has plenty of experience, having played international football and in the Premier League, so will add great quality to the players we already have in the squad.
"He will also enable us to be tactically flexible as he can play as the left-sided centre-back in a back three or back four as well as at left back, so it gives us great options to be able to play different systems if we feel we need to".