A jury at London's Southwark Crown Court found Butt, the former captain, guilty of both counts of conspiracy to cheat and conspiracy to accept corrupt payments.
Asif, 28, was found guilty of a single count of conspiracy to cheat. The judge ordered the jury to retire again to continue deliberating on the second charge against Asif.
Judge Jeremy Cooke ordered the jury, which had already spent a total 16 hours discussing its verdicts, to retire again to continue its efforts to reach at least a 10-2 majority decision on the second charge against Asif.
Butt, 27, and Asif plotted to bowl deliberate no-balls in the Lord's Test as part of a lucrative betting scam.
The pair were caught after an undercover reporter recorded the UK-based sports agent Mazhar Majeed, 36, boasting of how he could arrange for Pakistan cricketers to rig games for money
Butt could face seven years in jail when the pair are sentenced later this week. The lesser charge of conspiracy to cheat carries a possible punishment of two years imprisonment.
Butt, Asif and bowler Mohammad Amir already have received lengthy suspensions by an International Cricket Council anti-corruption tribunal in Doha for fixing parts of the Lord's test.
Butt was banned for 10 years, five of which are suspended, Amir was banned for five years and Asif was given a seven-year ban, with two suspended.
Cooke previously told the 12 jurors to accept that Amir was involved.
The jury initially retired at midday on Thursday but reported to Cooke on Monday that it was unable to reach a unanimous decision.
The allegations originally surfaced after Majeed was recorded by an undercover reporter working for the now-defunct News of the World tabloid saying that the three Pakistan players had accepted money to fix betting markets.
Majeed was secretly filmed accepting US$242,000 (Dh888,140) in cash from the journalist.
Butt said he had ignored the requests from Majeed, his agent, and Asif said he had only bowled the no-ball at precisely the time Majeed said it would be delivered because Butt had told him to run faster moments before bowling.