Beverley was an outstanding full-back and was eventually persuaded to join Blackburn Rovers. In the 1883-84 FA Cup Blackburn beat Padium (3-0), Staveley (5-0), Upton Park (3-0), and Notts County (1-0) to reach the final. Their opponents were Queens Park, the best team in Scotland. Joe Beverley played at right-back. The Scottish club scored the first goal but Blackburn Rovers won the game with goals from Blackburn lads, James Forrest and Joe Sowerbutts.
Joe Beverley won his first international cap for England against Ireland on 23rd February, 1884. England won 8-1. Beverley did very well and he retained his place against Scotland (15th March) and Wales (17th March).
In 1885 Beverley returned to Blackburn Olympic. The decision by the Football Association to allow clubs to pay their players increased their out-goings. It was therefore necessary to arrange more matches that could be played in front of large crowds. In March, 1888, William McGregor, a director of Aston Villa, circulated a letter suggesting that "ten or twelve of the most prominent clubs in England combine to arrange home and away fixtures each season." The following month the Football League was formed. It consisted of six clubs from Lancashire (Blackburn Rovers, Preston North End, Accrington, Burnley and Everton) and six from the Midlands (Aston Villa, Derby County, Notts County, Stoke, West Bromwich Albion and Wolverhampton Wanderers). The main reason Sunderland was excluded was because the other clubs in the league objected to the costs of travelling to the North-East.
Beverley rejoined Blackburn Rovers and took part in their first season of the Football League began in September, 1888. Preston North End won the first championship that year without losing a single match and acquired the name the "Invincibles". Blackburn finished in 4th place, 14 points behind Preston. Beverley, who was now 32 years old, only played in eight games and retired at the end of that season.
Joe Beverley died in 1897.