The area of the park was originally the swampy floodplain of the river, and was impossible to build on. The site first became home of the Dominion Rifle Range, where soldiers had trained before departing for the Second Boer War. This history is preserved in the name of Range Road, which runs along the west of the park. The area was turned into a park by the Ottawa Improvement Commission between 1904 and 1907. It was named after Lord Strathcona, a Canadian businessman and politician who had financed his own regiment in the Boer War.
The most prominent feature of the 15-acre (6.1 ha) park is the fountain standing atop the hill that was donated by Lord Strathcona in 1909, sculpted by Mathurin Moreau. The park's original design was a classic example of English public park design. It contained a pair of small ponds, gazebos, and Ottawa's first golf course. In the 1940s, the ponds were filled in due to their expense, and replaced with a wading pool. A baseball diamond was constructed at the southern end of the park in the 1920s and for many years was Ottawa's main venue for the sport.
The banks of the Rideau were once a popular swimming area, but today there is enough pollution, or perception thereof, to make this unpopular. During the summer the water level is low enough to ford the river and cross to Riverain Park in Vanier (although the Adàwe Crossing bridge, opened in December 2015, makes fording the river unnecessary). Just to the south of Strathcona Park is Dutchy's Hole Park and Robinson Field. In winter, the park, with its large hill at the northern end, is a popular site for tobogganing and making snowboard jumps.
The park remained under the control of the OIC successor agency the National Capital Commission until 1987 when it did not renew its lease with the city. Since then it has been a municipally managed park. In the early 1990s, the park was refurbished by the city. One of the most noted additions was the play structure designed by artist Stephen Brathwaite. Mr. Brathwaite designed a structure to look like ruins, inspired by Mackenzie King's ruin garden at Kingsmere. The structure was assembled out of blocks of stone that had been part of the parliament buildings, the Chateau Laurier, and other prominent Ottawa structures.
Since 1986, the park has been home to Odyssey Theatre, a professional company that presents open air plays each summer on a stage at the northeast corner of the park. Odyssey Theatre's unique performances of classical plays and original creations are inspired by the Italian Commedia dell’Arte and incorporate international forms of puppetry, clowning, and dance-theatre.
In July 2014, the city of Ottawa began construction of a pedestrian and cyclist bridge across the Rideau River connecting the Rideau River Eastern Pathway at Donald Street with Strathcona Park and Somerset Street East.
The park is surrounded by a series of large homes that once housed the elite of Ottawa. Today they are mostly embassies and the area around the park is often called Ottawa's Embassy Row. Perched above the park is the Russian embassy, formerly that of the Soviet Union.