Konate arrives on season from Russia side Krasnodar on a season-long loan, while Croatian international Vrsaljko joins Dinamo Zagreb for an undisclosed fee.
A number of Premier League clubs had been linked with Konate, but Genoa have managed to lure the 20-year-old to Italy with the option to make his loan move permanent.
"Moussa Konate joins Genoa on loan. The young player will defend the Serie A club colors in season 2013/2014", read a Krasnodar statement.
Right-back Vrsaljko is highly-regarded after impressing at Zagreb and he is already a Croatian international.