Becker told jurors he did not know the whereabouts of the memorabilia, including two of his three Wimbledon men's singles trophies.
Judge Deborah Taylor had released Becker -- who won Wimbledon as an unseeded teenager -- on conditional bail ahead of her sentencing decision on Friday.
Passing sentence, she told him: "You have not shown remorse, acceptance of your guilt and have sought to distance yourself from your offending and your bankruptcy.
"While I accept your humiliation as part of the proceedings, there has been no humility."
Taylor said Becker's previous conviction in Germany for tax offences was "a significant aggravating factor".
Becker arrived early for the hearing, wearing a striped purple and green tie in the Wimbledon colours, a white shirt and a charcoal grey suit.
He held hands with his partner Lilian de Carvalho Monteiro as he walked into court past a bank of waiting reporters and cameras.
The star showed no emotion as he was sentenced, picking up his bag before being taken down to the cells.
There was no immediate word that Becker would appeal and he will lodge any legal challenge from behind bars.
US women's tennis great Chris Evert responded to Becker's imprisonment by tweeting: "Sorry to hear about @TheBorisBecker... fun to work with on @eurosport and always a gentleman."
Former world number one Becker told the jury how his $50 million (£40 million) career earnings were swallowed up by a costly divorce from his first wife Barbara Becker, child maintenance payments and "expensive lifestyle commitments".
Becker said he was "shocked" and "embarrassed" when he was declared bankrupt in June 2017 over an unpaid loan of more than £3 million on his estate in Mallorca, Spain.
The German, who has lived in Britain since 2012, said he had cooperated with trustees trying to secure his assets, even offering his wedding ring, and relied on the advisers who managed his life away from tennis.
But the former player, who was supported in court by his partner and eldest son Noah, was found guilty of four charges.
Giving evidence, Becker said he earned a "vast amount" of money during his career, paying cash for several properties.
But the German, who went on to coach current world number one tennis player Novak Djokovic, work as a TV sports commentator and act as a brand ambassador for firms including Puma, said his income "reduced dramatically" following his retirement in 1999.
Becker, who was resident in Monte Carlo and Switzerland before moving to the UK, said his financial commitments included his £22,000-a-month rented house in Wimbledon, southwest London.
He also owed the Swiss authorities five million francs (about $5.1 million) and separately just under one million euros in liabilities over a conviction for tax evasion and attempted tax evasion in Germany in 2002.
He said bad publicity had damaged "brand Becker", meaning he struggled to make enough money to pay off his debts.
His lawyer Jonathan Laidlaw said at the time of his bankruptcy that Becker was too "trusting and reliant" on his advisers.
Becker, with a shock of strawberry-blond hair, shook up the tennis world in 1985 when he became Wimbledon's youngest men's singles champion at 17 and repeated the feat the following year.
Nicknamed "Boom Boom" Becker for his ferocious serve, he won Wimbledon for a third time in 1989.
He also won the Australian Open twice and the US Open during his glittering career, becoming the top-ranked player in the world in 1991.
Becker turned to commentary after his retirement, landing a high-profile role on the BBC, but he returned to the court in 2013 to guide Djokovic, helping the Serb win six more Grand Slam trophies before the pair parted ways in 2016.