Efforts to fill vacancies in Boston’s 1.1-million-square-foot 53 State St. office tower following law firm Goodwin Procter’s departure continue, with four new tenants signing leases for over 103,000 square feet.

Health care consultants Press Gainey Assoc. are relocating from 401 Edgewater Place in Wakefield to 10,401 square feet at the 40-story tower.

Professional services firm Aon leased 39,229 square feet in a relocation from One Federal St., the Institute for Healthcare Improvements is relocating from 20 University Road in Cambridge to 26,962 square feet and Experian Information Solutions committed to 26,970 square feet in a move from 125 Summer St.

Following the latest transactions, the building has approximately 200,000 square feet available, said Glenn Verrette, executive director for Cushman & Wakefield which represents ownership.

UBS acquired the 40-story tower in 2011 from Brookfield Properties for $610 million.

Prompted by the departure of Goodwin Procter for a new office tower developed by The Fallon Co. at 100 Northern Ave., UBS launched a capital improvements program including a new tenant conference space and roof deck and added Squeeze Café.

Cushman & Wakefield has completed 31 transactions in the building for more than 659,000 square feet under UBS ownership including leases by law firm Rubin and Rudman, cloud computing company Acquia and The Boston Globe’s editorial and business departments.

Verrette and Senior Director John McHugh represented ownership in all four leasing transactions.

“The new amenities definitely played a factor and the roof deck has been very well-received by the existing tenants and prospects that are considering the building,” Verrette said.

Owners have promoted the property’s proximity to multiple MBTA lines and a central downtown location in a corner of the Financial District that’s seeing substantial change. Across Congress Street, a portfolio of former Fidelity Investments office buildings are being redeveloped into housing, a hotel, ground-floor retail and creative office space.

At the opposite end of Post Office Square, Boston Properties is expanding its 100 Federal St. tower with a new ground-level glass atrium with retail and food vendors.