Rubuta ci gaba don wannan sakin layi - Vesalainen ya fara wasa a matsayin matashi a ƙasarsa ta Finland, yana bayyana har zuwa matakin Junior A tare da HIFK kafin ya zaɓi ya ci gaba da ci gabansa a Sweden tare da Frölunda HC a ranar 27 ga Agusta 2015. Vesalainen ya fara wasan sa na farko a matakin manyan 'yan wasa tare da Frölunda a gasar Hockey ta Sweden a lokacin kakar 2015-16. Bayan lokacin aro na farko don komawa Finland a lokacin kakar 2016/17 tare da HPK na Liiga, Vesalainen ya sanya matsayinsa na dindindin ta hanyar yarda da yarjejeniyar shekara guda tare da HPK a ranar 28 ga Afrilu 2017. A cikin shekararsa ta farko na cancanta, an zabi Vesalainen a zagaye na farko, na 24 a duka, ta Winnipeg Jets a 2017 NHL Entry Draft
a ranar 23 ga Yuni, 2017.