The Australia defender has joined on a free transfer from Dinamo Moscow while the Netherlands youth international has signed a four-year deal from Herenveen
Australia international Wilkshire joins on a free transfer following his release from Russian outfit Dinamo, signing a one-year deal with an option to extend that by a further 12 months.
The 32-year-old previously enjoyed a spell in the Premier League with Middlesbrough, before stints at Bristol City and Twente ahead of a move to Dinamo in 2008.
Basacikoglu has signed a four-year contract with the option of another year.
The Netherlands Under-19 international scored six goals in 24 Eredivisie appearances for Heerenveen last season.
"Our policy is aimed to fill with great talents from outside," technical director Martin van Geel told the club's official website.
"We are very happy with the arrival of Bilal Basacikoglu, a multi-year contract signing who will get the chance to develop further.
"We believe that talent can only develop on the basis of experienced players. In that respect, Luke Wilkshere is a very welcome reinforcement."
The arrivals of Wilkshire and Basacikoglu will come as a welcome site for Feyenoord fans, who have seen Stefan de Vrij, Daryl Janmaat, Bruno Martins Indi and Graziano Pelle all leave the club so far this summer.