Alexandersson became Middle DistanceJunior World Champion in orienteering in 2009. She was 16 years old at the time, running against competitors up to four years older than her. She maintained her Middle Distance title in both 2010 and 2012, with two further gold medals in the sprint and in the relay, two silvers, and one bronze in the long distance.
After her success as a junior prodigy Alexandersson took several years to achieve her gold medal, receiving only silvers and bronzes in 2011, 2012, 2013, 2014 and 2015 despite being one of the favourites. She made her breakthrough in 2016, a season which saw her take #1 in the world ranking as well as dominate in the Orienteering World Cup and the World Orienteering Championships, where she won both individual forest titles. In 2017 she continued to dominate at the 2017 World Orienteering Championships in Estonia, where she won all forest classes. In the 2018 WOC she won the silver medal in sprint and the gold medal in mixed sprint relay. In the 2019 WOC she won the gold medals in the long and middle distances and also participated in the winning Swedish relay team together with Lina Strand and Karolin Ohlsson. She also won the Venla Relay in 2018 together with Julia Gross, Anna Mårsell and Magdalena Olsson.
Alexandersson won both forest European Orienteering Championships titles in 2016. In 2018 she won the gold medals in sprint and long distance and the silver medal in the middle distance.
Ski orienteering
She won a gold medal in the sprint distance at the 2011 World Ski Orienteering Championships in Sweden. In 2015, she once again won the women's World Ski Orienteering Championships sprint distance event. Alexandersson is one of very few orienteers who participate in both ski orienteering and the more popular foot orienteering. Alexandersson has been dominant in ski orienteering in recent years; at the championships in Russia in 2017 she won three gold medals. In December 2018, Alexandersson became the first athlete to be ranked #1 in three separate disciplines by the International Orienteering Federation.
Skyrunning
In 2017 Alexandersson took a surprise victory in the 29 kilometer Limone Extreme SkyRace with a margin of 12 minutes ahead of established skyrunning specialists, and despite taking several downhill running falls that required medical attention to arms, hands and legs. In September 2018 Alexandersson won a gold medal in the Sky discipline of the biennial Skyrunning World Championships held on the Ring of Steall Skyrace course at Kinlochleven in Scotland. She won by more than seven minutes, setting a new course record by 19 minutes on the demanding and technical course with about of climb. Said Alexandersson: "I did not have a big expectation of this race because I am new to skyraces but it was a nice day for me. It was a fantastic course and it feels amazing to be world champion." In October 2018 Tove Alexandersson triumphed for the second year in a row in the Limone Extreme SkyRace, this time by a margin of nine minutes. This was Alexandersson's third skyrunning race ever, and she remained undefeated.
Ski mountaineering
In November 2019 Alexandersson stated that she would limit her ski orienteering competitions during the upcoming winter, in order to practice ski mountaineering. She said that she intended to participate in five world cup competitions plus the upcoming European Championships.
