As well as minor public order offences, 10 of the arrests concerned alleged sectarian breaches of the peace.
Eleven men are expected to appear at Glasgow Sheriff Court on Monday; five others are subject of a report to the procurator fiscal; three were issued with a fixed penalty notice.
Police said the behaviour of most fans at the game was "excellent".
Match commander Ch Supt Andy Bates said: "As usual the vast majority of the 50,000 fans were here to enjoy the game and support their respective team; they deserve credit for their excellent behaviour.
"However, again, it is the minority of fans who spoiled the occasion by for example setting off flares and singing sectarian songs.
"We dealt with any incidents swiftly and with minimum disruption. As at 1700 hours, 19 men have been arrested for a number of offences - mostly alleged minor public order offences but include 10 arrests for alleged sectarian BOPs (breaches of the peace)."
Police have said 19 men were arrested for offences connected with the Celtic-Rangers football match in Glasgow.