Taken from wikipedia.
Arsenal Football Club started out as Dial Square in 1886 by workers at the Royal Arsenal in Woolwich, south-east London, and was renamed Royal Arsenal shortly afterwards.[4] The club was renamed again to Woolwich Arsenal after becoming a limited company in 1893.[5] The club became the first southern member of the Football League in 1893, starting out in the Second Division, and won promotion to the First Division in 1904. The club's relative geographic isolation resulted in lower attendances than those of other clubs, which led to the club becoming mired in financial problems and effectively bankrupt by 1910, when they were taken over by businessmen Henry Norris and William Hall.[6] Norris sought to move the club elsewhere, and in 1913, soon after relegation back to the Second Division, Arsenal moved to the new Arsenal Stadium in Highbury, North London; they dropped "Woolwich" from their name the following year.[7] Arsenal only finished in fifth place in 1919, but were nevertheless elected to rejoin the First Division at the expense of local rivals Tottenham Hotspur, by reportedly dubious means.[8]
I don't pretend to understand all that went on over the Wimbledon move but they weren't the first and won't be the last.