Electrostatic solitary waves (ESWs) in the Venusian ionosphere that are impinged by the solar wind are investigated using a homogeneous, collisionless, and magnetized multicomponent plasma consisting of Venusian H+ and O+ ions, Maxwellian Venusian electrons and streaming solar wind protons, and suprathermal electrons following κ − distribution. The model supports the propagation of positive potential slow O+ and H+ ion-acoustic solitons. The evolution and properties of the solitons occurring in two sectors, viz., dawn-dusk and noon-midnight sector of the Venus ionosphere at an altitude of (200–2000) km, are studied. The theoretical model predicts positive potential solitons with amplitude ∼(0.067–56) mV, width ∼(1.7–53.21) m, and velocity ∼(1.48–8.33) km s−1. The bipolar soliton electric field has amplitude ∼(0.03–27.67) mV m−1 with time duration ∼(0.34–22) ms. These bipolar electric field pulses when Fourier transformed to the frequency domain occur as a broadband electrostatic noise, with frequency varying in the range of ∼9.78 Hz–8.77 kHz. Our results can explain the observed electrostatic waves in the frequency range of 100 Hz–5.4 kHz in the Venus ionosphere by the Pioneer Venus Orbiter mission. The model can also be relevant in explaining the recent observation of ESWs in the Venus magnetosheath by the Solar Orbiter during its first gravity assist maneuver of Venus.