Major General Jonathan Shaw told the Guardian that the number of successful attacks was hard to quantify, but they had added urgency to efforts to improve protection of the MoD's networks.
Although government systems are under daily attack, this is the first time the MoD has admitted that its top secret systems have been breached, the paper said.
Shaw said the number of known serious incidents was "quite small", but admitted that there may be some that are still unknown.
In November, he told a cybersecurity conference in London that the UK was still operating in pre-cyber attack mode, but that needed to change before it was hit by a major cyber attack.
"The UK should learn from Estonia, hit by a wave of cyber attacks in 2007, which operates a virtual cyber defence system in post-attack mode that harnesses all cyber users," he said.
On a visit to Estonia this week, Cabinet Office minister Francis Maude said he would be discussing ways in which the two countries can share their experience in increasing business and government's resilience to cyber attack.
Commenting on the breaches at the MoD, Shaw said the military could learn from firms such as Facebook, which has set up a "white hat" program in which hackers are paid rewards for informing them when they have found a security vulnerability.
An MoD spokesman said: "The MoD takes all possible precautions to defend our system from attack from both unsolicited, for example 'spam' email, and targeted sources.
"It would be both misleading and naïve to assume that any system is 100% secure against all possible threats which is why we take additional steps to detect suspicious activity within our own systems.
"We also ensure that our most sensitive networks are not connected to the internet and have additional physical and technical measures in place to defend them."
This story was first published by Computer Weekly