Exoplanets have become a major focus in astronomy over the last two decades which has driven a rapid increase in the number of detected exoplanets. The detection of new exoplanets will drive the future of astronomy. Our understanding of planetary formation, the conditions for extraterrestrial life, and the location of habitable worlds are directly dependent on obtaining high-quality observations of exoplanets. There are a number of methods used to detect an exoplanet through direct and indirect observations. Direct detection of an exoplanet is done by observing the exoplanet itself, while indirect detection is done by observing changes in the star or circumstellar disk. No single detection method can determine everything about an exoplanet, and each is biased toward certain kinds of planets. The work presented here focuses on the problem of directly detecting exoplanets that have been discovered indirectly via the "radial velocity" method. The first part of the dissertation focuses on how to calculate the times when a planet with an orbit fitted via the radial velocity detection method will be detectable for a direct imaging telescope. The dissertation analyzes how to convert the orbit fits, estimate the probability of detection as a function of time, and identifies two major failure modes inherent to the process. The second part of the dissertation identifies a problem with a traditionally used method of calculating the dimmest planet that can be detected for a given integration time, the observing time spent collecting photons for science. In creating higher fidelity models of the signal to noise ratio for exoplanet detection, the signal and noise terms have become inseparable which makes it impossible to calculate the dimmest planet detectable as a function of integration time analytically. The dissertation demonstrates a numerical routine to solve this problem and uses the numerical routine to calculate the performance of the Roman Space Telescope's different observing scenarios on known exoplanets. Finally, the dissertation uses the numerical routine to determine the dimmest planet detectable to create a more accurate model to estimate the probability of directly imaging an exoplanet detected via the radial velocity method by accounting for additional sources of noise. The probability is found by using the dimmest planet detectable over a direct imaging instrument's possible planet-star separations, local zodiacal light values, and exozodiacal light values and comparing those values to the estimated positions and brightnesses of planets consistent with the underlying radial velocity data. The probability of detection metric is validated by creating a framework for full simulations of the process. The framework generates a set of radial velocity data for synthetic exoplanets, fits orbits to the radial velocity data, calculates the probability of detection, schedules observations, and simulates the observations. The scheduling algorithm is validated with a simulation of future radial velocity and direct imaging instruments. In the simulation the scheduling algorithm is compared against random searches and the algorithm, on average, detects approximately 32 unique planets in approximately 375 days of integration time while a random walk detects approximately 17 unique planets in approximately 720 days of integration time. Finding twice as many planets in half the time is a significant improvement and proves that direct imaging observations of previously detected planets can be reliably scheduled with the assumed instrument performance and mission design parameters.