Career criminal Craig Sibson was locked up for 16 months for the 'mean' offences committed against the vulnerable victims.
Sibson, 49, managed to obtain the couple's bank card and withdrew cash on a regular basis.
Leeds Crown Court heard Sibson carried out the offending after befriending the pensioners at their home on Easterly Road, Leeds.
The offending came to light following the death of the woman in 2017.
Her husband suffered from dementia and their daughter took over responsibility for his financial affairs.
Austin Newman, prosecuting, said the daughter was shocked to discover her father's bank account was overdrawn.
She had expected there to be in excess of £10,000 in the account.
The daughter found notebooks which had belonged to her mother which referred to sums of money owed to her by 'Andrew' and 'Carl'.
Sibson was identified as Andrew by a neighbour who said he had been a regular visitor to the couple's home.
The neighbour described how on one occasion he had helped the husband look for his bank card after it went missing.
The court heard the husband asked the defendant if he had his bank card but he claimed not to have it.
Sibson went into the property and 'made a show' of finding the card.
The neighbour described how he became suspicious as he had already searched the area of the house where Sibson claimed to have found the card.
Investigations revealed Sibson withdrew a total of £746 on 26 occasions using the couple's bank card between August and September 2017.
Sibson was identified on CCTV footage withdrawing cash from machines.
Mr Newman said it was estimated that the couple had lost a total of £20,000 but it was "impossible to attribute the whole of that loss to the defendant."
The court heard others are also believed to have been involved in taking money from the couple.
Sibson, of Elmete Way, Roundhay, pleaded guilty to theft and transferring criminal property.
The prosecutor said Sibson pleaded guilty to the later offence on the basis that he had obtained cash transfers to the value of £9,000.
Sibson has 32 convictions for 72 previous offences.
He has served previous prison sentences for targeting elderly victims.Stephen Welford, mitigating, said: "He's 49 now and it is perhaps a miracle that he is still with us, having used class A drugs since the age of 19."
Mr Welford said Sibson had not been in trouble since the offending and had the support of his family.
Sibson was jailed for 16 months.
Judge Neil Clark said the offending was so serious that only an immediate custodial sentence could be justified.
He said: "This was very mean and unpleasant offending.
"You befriended this elderly couple and gained their trust.
"It is not the loss of money that hurts people. It is the psychological impact of knowing that someone has been so mean and so devious to members of their family that hurts.
"It must be immediate custody for someone who commits an offence as mean and despicable as this."