Plans to employ a marksman to shoot the pied wagtail at the Great Yarmouth store were put on hold after TV star Chris Packham tweeted his opposition.
The British Trust for Ornithology said it had been caught, with Mr Packham tweeting a photo of the "renegade".
Tesco said shooting the bird was only considered as a last resort.
Natural England granted the firm a licence to shoot the wagtail earlier this month on the grounds of public health after it was spotted in the shop's aisles.
But Mr Packham, who presents BBC Springwatch, used his Twitter account to urge Tesco to get in touch with the BTO instead, to attempt to catch the bird safely.
Tesco said many attempts to catch it had failed, but tweeted it was "happy to liaise with BTO and explore other options".
The BTO confirmed it had been caught earlier after putting up a giant net in the store.
Pied wagtails are typically 18cm (7in) long and weigh 21g (three-quarters of an ounce). There are 470,000 breeding pairs in the UK.
They are protected by the Wildlife and Countryside Act, with anybody who kills one without a licence facing a Â£5,000 fine.

Downing Street and the White House are believed to be looking at options for the visit.
Mr Trump accepted the Queen's invitation for him to travel to Britain on a state visit when UK PM Theresa May visited Washington in January.
But the prospect of a state visit caused much controversy and reportedly led Mr Trump to change his mind.
It was said he did not want to visit while there was potential for protests against him.
Nearly two million people signed one of a number of petitions saying Mr Trump should not be invited to the UK on a state visit.
What is a state visit?
Senior politicians, including Labour leader Jeremy Corbyn and former Lib Dem leader Tim Farron who called Mr Trump "an embarrassment to America", said the visit should not go ahead.
Questions were also raised as to why Mr Trump was invited so soon after taking office - it was two-and-a-half years into his first term before his predecessor Barack Obama came to the UK for his state visit.
Mrs May extended the invitation to the president just as he sparked anger across the world with his proposed travel ban on visitors from seven predominantly Muslim countries.
The mayor of London, Sadiq Khan, clashed with Mr Trump over the immigration measures, later saying the UK should not "roll out the red carpet to the president of the USA in the circumstances where his policies go against everything we stand for".
Confirmation of Mr Trump's visit had been expected in last month's Queen's Speech, in which the Queen set out her official plans for the year.
But there was no mention of it, and October was later mooted as a possible date.
The White House denied reports that Mr Trump had reservations about visiting, saying they looked forward to working out a "mutually acceptable date".
The Queen usually receives one or two heads of state a year. She has hosted 109 state visits since becoming monarch in 1952.
State visits are grand, ceremonial occasions, but have a political purpose too, with governments using them to further what they see as Britain's national interests.

Led by Durham Wildlife Trust, the scheme will see a preservation plan drawn up for the River Skerne.
It will include initiatives to protect natural habitats as well as industrial and agricultural sites.
If successful, organisers say a further £2.6m from the Heritage Lottery Fund will be unlocked as well as £500,000 from other sources.
The project, called the Bright Water Landscape partnership, covers 200sq km (77sq miles) and focuses on the River Skerne from Hurworth Burn reservoir in East Durham to South Park in Darlington.
A small bird that earned a last minute reprieve after supermarket giant Tesco retracted a bid to shoot it has been caught and released.
[NEXT_CONCEPT]
US President Donald Trump is likely to come to the UK next year, the BBC understands.
[NEXT_CONCEPT]
A project to conserve a North East river catchment area has been awarded £223,000 of Lottery funding.