The men intercepted business and personal cheque books and cards in the post and changed payee names and forged sums to be paid in.
Leeds Crown Court heard one fraudster, Effart Diza, of Knowle Terrace, Harehills, was exposed after trying to pay in a £136,000 forged cheque into a bank account set up by the men.
A jury convicted Diza of conspiracy to defraud after a trial. He was jailed for five-and-a-half years. Naison Mubaiwa, 35, of Grange Avenue, Harehills, was jailed for three and a half years after admitting conspiracy to defraud.
Paddington Muzundiwa, 25, of Manchester, was jailed for two years after admitting the same charge. All three men had failed to win asylum in the UK.
Prosecutor Timothy Capstick said total losses to banks and financial institutions including HBOS amounted to over £1m.
Police searched a string of addresses linked to the defendants where they found evidence linking the men to the fraud including cheque books, cards and typewriters and computers used to forge documents.
Jailing the three men, Judge Kerry Macgill said: "This was by anyone’s standards a large scale and sophisticated conspiracy. This was fraud on a grand scale."
A fourth man, Charles Kanyimo, 35, of Wakefield, was previously jailed for three years after he pleaded guilty to two counts of conspiracy to defraud.
The arrests were made as part of an operation that saw warrants executed at 30 addresses in West Yorkshire and around the country.