The Black Cats have agreed terms with out-of-contract Coventry goalkeeper Westwood and Birmingham midfielder Larsson, who remain contracted to their current clubs until June 30 but will officially become Sunderland players on July 1.
A club statement said: "Sunderland AFC today confirmed that terms have been agreed with Republic of Ireland goalkeeper Keiren Westwood and Swedish international midfielder Sebastian Larsson.
"The players will officially sign with the club on July 1, 2011."
Westwood was on Wearside earlier this week to finalise the deal and undergo a medical, and fellow 26-year-old Larsson followed him on Wednesday as Bruce finally tied up two deals which he had been pursuing for several weeks.
There were suggestions that the Black Cats could face late competition for Larsson from Aston Villa, now managed by former Birmingham boss Alex McLeish, but they moved swiftly to get their man today.
Bruce had identified the pair as two of three Bosman signings he hoped to make during the early weeks of the summer transfer window, and having missed out on Lorient midfielder Morgan Amalfitano, will be delighted to have succeeded.
The Black Cats will now concentrate on their remaining targets, with efforts to recruit South Korea striker Ji Dong-won ongoing despite his club Chunnam Dragons confirming his imminent departure in a statement.
It said: "Ji Dong-won is joining Sunderland on a three-year contract.
"The terms negotiated by the two clubs regarding transfer fee and salary will not be released publicly."
Ji is yet to head for Wearside and has therefore not undergone a medical, but work is continuing behind the scenes.
The striking department will be Bruce's main priority for the summer after he finished last season with Asamoah Gyan as his only fit frontman.
Loan signing Danny Welbeck has returned to parent club Manchester United and hopes to have a role to play at Old Trafford next season, while Fraizer Campbell will be sidelined by his latest knee injury for much of the new campaign.
Sunderland have now firmed up their interest in Ipswich's Connor Wickham with a bid, although the 18-year-old has many admirers and there is sure to be a battle for his signature if the Suffolk club decide to sell.
In addition, they are pursuing their interest in United trio Darron Gibson, Wes Brown and John O'Shea, who were the subject of a joint £12million-plus bid earlier this month.