The judge ordered that the Romanian be deported at the end of his sentence
Stefan Neagu, 39, was arrested after one fan at the Korn and Limp Bizkit gig last month caught him in the act and alerted staff at the Manchester Arena venue.
British Transport Police officers uncovered Neagu's haul, which was concealed underneath his clothes.
Neagu, of no fixed address, pleaded guilty to the thefts and was sentenced to three months in jail at Manchester Crown Court.
The sentencing judge ordered the defendant should be deported at the end of his sentence.
Investigating officer Detective Constable Richard King said: “Neagu preyed on and took advantage of unsuspecting music fans who were enjoying a concert.
The 19 phones were stolen during a Limp Bizkit and Korn concert
Neagu preyed on and took advantage of unsuspecting music fans
Detective Constable Richard King
“Thanks to the immediate reporting of an unsuccessful theft and a detailed description, we were able to arrest Neagu as he was leaving the venue.
"This meant we retrieved the haul of mobile phones and have so far managed to return 15 to their owners.
“We use a variety of tactics to deter organised crime gangs from targeting events like these and share information with other agencies in the UK and abroad in a bid to apprehend those responsible.
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Neagu was caught in the act by a rock fan, who alerted security
“Thieves and pickpockets like Neagu are drawn to busy environments as their victims are often distracted. Our advice to anyone in a crowded, busy place, whether it be a station, train or music venue, is to keep your valuables hidden away and secure at all times.
“While Neagu is now behind bars, our war on theft continues and pickpockets always have their eye on the next target. Let's make life difficult for them by keeping temptation out of sight.”