The £318m settlement includes £230m in damages, as well as £40m in interest and tax, already paid by HP.
HP acquired EDS in 2008, when it was embroiled in a legal battle with the broadcaster.
In a judgement delivered in January, EDS was found to have deliberately lied about the time needed to complete the customer software implementation at the broadcaster.
These lies helped it win the £48m deal ahead of PricewaterhouseCoopers, the judge found.
The final sum also includes legal costs and remaining damages claimed by BSkyB, issues that had been hotly contested.
HP is also believed to have run up legal costs of around £40m, fighting the case, a similar expenditure to BSkyB. HP did not confirm the figure.
HP will now make a final £48m payment to BSkyB.
The news comes days after HP said it would cut 9,000 jobs as part of efforts to reinvigorate its IT services division – including EDS – and three months after HP was forced to restate revenues after the original £270 million was paid.
The total payment of £318m fepresents more than a fifth of HP's entire net earnings for services, PCs and printers for the last quarter to 30 April.
"On June 7 2010, EDS and Sky fully and finally settled the litigation between them and all related claims (including for damages, costs and interest) for a total amount of £318m," BSkyB said.
"This amount includes the interim payments of £270m that EDS has already made to Sky in February 2010."
HP said the matter was now closed, "having been settled fully and finally on mutually agreed terms." It declined to give further details.
The lawsuit reached court in 2007, after extensive wrangling between EDS and BSkyB over the failed project.
Although work had begun by 2000, problems quickly began to emerge as BSkyB contested the rate of the work and the resources available.
A Letter of Agreement was signed in 2001 in order to set a clear path for the project.
It was after this point, following a history of problems between Sky and EDS, that the service provider was judged to have made some of the most damning errors.
EDS "failed properly to resource the project" after this point, and was "seriously in delay" with regard to milestones, the judge wrote in his judgement.
In the eight months to March 2002, when EDS' work was terminated, it had done "little work".
While the failures did not constitute a repudiatory breach, the judge said that EDS "failed to exercise reasonable skill and care or conform to good industry practice".
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There was "no effective programme management, the design and development of the solution was not properly documented and EDS did not provide sufficient technical or managerial resources", in the period, he said.
Sky took over the project's leadership in 2002, around the time the CRM system was supposed to have been complete. In the end it took until March 2006, and cost £265m, over five times the original budget.