Homeownership is an important indicator of immigrant incorporation. Using administrative data from Sweden (1997–2016), we investigated entry into first-time homeownership across immigrant groups and generations. We differentiated between immigrants arriving as adults (1 G) and children (1.5 G) and between descendants of immigrants with two (2 G) and one (2.5 G) foreign-born parent(s). Immigrants from sub-Saharan Africa showed the lowest propensity to move to homeownership, whereas immigrants from Nordic countries, Western-Europe and North America had the highest likelihood. A large proportion of immigrants moved to first-time homeownership already in their first year in Sweden. We observed a clear gradient across migrant generations: the 2.5 G had homeownership levels closer to native Swedes than the other generations, although they still had lower homeownership than the native population. The observed differences in homeownership between the descendants of immigrants from high- and low-income countries suggest the presence of housing segregation due to migration background, preferences, and available resources. These differences, however, are reduced over time and across migrant generations. This study advances the international housing scholarship by highlighting generational convergence of immigrant homeownership in Sweden. Additionally, it offers evidence on the long-term role of homeownership access in shaping social inclusion and incorporation across diverse migrant populations.