The Southampton-born custodian has been brought in as the first-choice replacement for outgoing captain Adam Davies, whose move to Stoke City will be officially announced shortly.
Collins, who impressed in a productive loan spell at Burton Albion last term, which saw him make 35 appearances and keep 11 clean sheets, represented Barnsley's first-choice option to replace Davies.
He was recently freed by the Stamford Bridge outfit, having first joined the club at under-21 level.
The 22-year-old also enjoyed a fruitful stint on loan at Forest Green in 2017-18, which saw him play 39 games for the Gloucestershire outfit.
On his move, Collins, whose deal includes a further option in the Reds' favour, said: “You just want to keep progressing as a footballer and if you look at my stats at the moment, it shows I have.
"I want to keep going and see how far we can go together here now. The vision here is good, there’s a good group of lads here who are hungry and play the right way.
"I have heard great things about the gaffer so I am really looking forward to working with him and I like the overall vision of the club.”
Co-chairman, Paul Conway said: "We are really pleased to welcome Brad to the club. He’s joined us at an exciting time and he comes with a strong record of nearly 100 EFL matches which is fantastic experience at a young age.
"We feel he can develop further here and grow with the club. The four-year contract, with the further additional option year, is another example of our strategy of securing our players to long-term deals.”
Collins is Barnsley's third close-season signing following the additions of Mike-Steven Bahre and Luke Thomas.
Meanwhile, Liam Lindsay's £2.5million move to Stoke is likely to be confirmed shortly.