Davis pleaded guilty to possession of a firearm contrary to Section 57 of the Terrorism Act 2000, and two charges of funding terrorism between 2013 and 2014.
The defendant entered his pleas via video link from Belmarsh prison.
Judge Lucraft adjourned sentencing until November 13.
The offences were largely uncovered from his communications with his then-wife, mother-of-two Amal El-Wahabi, 36, who stayed behind in north London living on benefits.
Davis, who used the name Hamza after converting to Islam, was born in the capital and spent time living in Saudi Arabia and United Arab Emirates in 2007.
He met El-Wahabi at a London mosque and they became increasingly interested in Islam.
In July 2013, he travelled to Syria but maintained regular contact with El-Wahabi by phone and internet.
He went on to enlist her in a plan to send him cash by hoodwinking her friend Nawal Masaad, 36, to act as courier on the promise of 1,000 euros.
Ms Masaad, from Holloway, north London, was stopped at Heathrow Airport on January 16 2014 as she was about to board a flight to Istanbul with 20,000 euros stuffed inside her tights.
The prosecution alleged the money raised in the UK was destined to support Davis’s terrorist cause in Syria.
Following El-Wahabi’s arrest in London, police uncovered a stash of terrorist propaganda said to have been left behind by Davis when he went to Syria.
On her mobile phone was a picture sent by Davis in November 2013 in Syrian woods with a man holding a Kalashnikov rifle.
Davis told his wife: “Don’t show this to anyone but yuyu. (sic). I mean it.”
He sent another picture posing with 13 others in military-style clothes, all with guns held aloft.
Asked by El-Wahabi if he was doing anything exciting, Davis said he was just “on point”, which is believed to be a reference to guard duty.
The court heard it was clear that Davis – who had convictions for possession of drugs and gun possession – had gone to Syria to fight under the black flag of IS and that he was preoccupied with martyrdom.
Giving evidence in her trial, El-Wahabi claimed Davis was “always there” for her and had left the country “to get away from everyone and to look for work”.
He was unhappy in London because of “the drugs, the influence of friends he has around him, the police targeting him constantly”, she said.
She added: “With him, his problem is he is always being watched.”
After the Old Bailey trial in 2014, El-Wahabi was found guilty of funding terrorism and jailed for 28 months, while Ms Masaad was cleared of wrongdoing.
El-Wahabi was the first person to be convicted of funding terrorism in Syria.
In November 2015, Davis was arrested with others in Istanbul after being found using a forged travel document and later jailed for IS membership.
Davis has always denied being connected with The Beatles cell – so-called because of their British accents – which tortured and beheaded western hostages in Syria.
Two IS Beatles members, British nationals El Shafee Elsheikh and Alexanda Kotey, are now seving life in US jails.
The third Beatle, Mohammed Emwazi, dubbed Jihadi John, who was believed to feature in shocking videos of IS beheadings of a number of captives, was killed in a drone strike in 2015.